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MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. Example: Find the mode of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. Example: Find the mode of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 8 appears more often (4 times) than any other number. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. Example: Find the mode of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 8 appears more often (4 times) than any other number. The mode is 8. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 2 numbers appear equally frequently, weβll call both of them modes. For a case like this, we say that the set of numbers is bimodal. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 2 numbers appear equally frequently, weβll call both of them modes. For a case like this, we say that the set of numbers is bimodal. Example: Find the mode of 7 , 7 , 2 , 7 , 1 , 5 , 2 , 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 2 numbers appear equally frequently, weβll call both of them modes. For a case like this, we say that the set of numbers is bimodal. Example: Find the mode of 7 , 7 , 2 , 7 , 1 , 5 , 2 , 2 2 and 7 are tied (at 3 times) for the most frequent number in the list. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 2 numbers appear equally frequently, weβll call both of them modes. For a case like this, we say that the set of numbers is bimodal. Example: Find the mode of 7 , 7 , 2 , 7 , 1 , 5 , 2 , 2 2 and 7 are tied (at 3 times) for the most frequent number in the list. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 2 numbers appear equally frequently, weβll call both of them modes. For a case like this, we say that the set of numbers is bimodal. Example: Find the mode of 7 , 7 , 2 , 7 , 1 , 5 , 2 , 2 2 and 7 are tied (at 3 times) for the most frequent number in the list. The modes are 2 and 7. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 3 or more numbers appear equally frequently, we will just agree to say that there is no mode. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 3 or more numbers appear equally frequently, we will just agree to say that there is no mode. Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 3 or more numbers appear equally frequently, we will just agree to say that there is no mode. Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3 2, 3 and 5 are tied (at 2 times) for the most frequent number in the list. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 3 or more numbers appear equally frequently, we will just agree to say that there is no mode. Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3 2, 3 and 5 are tied (at 2 times) for the most frequent number in the list. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 3 or more numbers appear equally frequently, we will just agree to say that there is no mode. Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3 2, 3 and 5 are tied (at 2 times) for the most frequent number in the list. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 3 or more numbers appear equally frequently, we will just agree to say that there is no mode. Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3 2, 3 and 5 are tied (at 2 times) for the most frequent number in the list. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MODE: The most frequent number in the set of numbers. If 3 or more numbers appear equally frequently, we will just agree to say that there is no mode. Example: Find the mode of 1 , 2 , 2 , 5 , 4 , 3 , 5 , 3 2, 3 and 5 are tied (at 2 times) for the most frequent number in the list. There is no mode. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 The simplest way to find the median is to put the numbers in order. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 The simplest way to find the median is to put the numbers in order. From small to large, we have: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 The simplest way to find the median is to put the numbers in order. From small to large, we have: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 The middle number is 5. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 The simplest way to find the median is to put the numbers in order. From small to large, we have: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 The middle number is 5. The median is 5. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9 Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9 Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9 This time there are 2 middle numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency WhenFor this any happens theπmedian is defined set of numbers to be the average of the 2 middle numbers. π₯51+, π₯82 , π₯13 3 β¦ , π₯π = = 6.5 There are 3 common2measures of central tendency. 2 MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9 Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9 This time there are 2 middle numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency WhenFor this any happens theπmedian is defined set of numbers to be the average of the 2 middle numbers. π₯51+, π₯82 , π₯13 3 β¦ , π₯π = = 6.5 There are 3 common2measures of central tendency. 2 MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9 Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9 This time there are 2 middle numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency WhenFor this any happens theπmedian is defined set of numbers to be the average of the 2 middle numbers. π₯51+, π₯82 , π₯13 3 β¦ , π₯π = = 6.5 There are 3 common2measures of central tendency. 2 MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9 Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9 This time there are 2 middle numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency WhenFor this any happens theπmedian is defined set of numbers to be the average of the 2 middle numbers. π₯51+, π₯82 , π₯13 3 β¦ , π₯π = = 6.5 There are 3 common2measures of central tendency. 2 MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9 Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9 This time there are 2 middle numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency WhenFor this any happens theπmedian is defined set of numbers to be the average of the 2 middle numbers. π₯51+, π₯82 , π₯13 3 β¦ , π₯π = = 6.5 There are 3 common2measures of central tendency. 2 MEDIAN: The middle number (in value) in the set of numbers. But what if there is no single number in the middle? Example: Find the median of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 , 9 Ordering the numbers, we get: 1 , 3 , 3 , 3 , 5 , 8 , 8 , 8 , 8 , 9 This time there are 2 middle numbers. The median is 6.5. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Before doing an example, letβs look at notation often used for the mean. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Before doing an example, letβs look at notation often used for the mean. π₯ MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Before doing an example, letβs look at notation often used for the mean. π₯ This is the standard mathematical symbol for the mean. It is pronounced βx barβ. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Before doing an example, letβs look at notation often used for the mean. π₯ This is the standard mathematical symbol for the mean. It is pronounced βx barβ. π₯1 + π₯2 + β― + π₯π π₯π π₯= = π π MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Before doing an example, letβs look at notation often used for the mean. π₯ This is the standard mathematical symbol for the mean. It is pronounced βx barβ. π₯1 + π₯2 + β― + π₯π π₯π π₯= = π π MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Technically, statistics, the sample mean. Forinany set ofπ₯πisnumbers If we draw a random sample π₯1from , π₯2 , aπ₯3population, β¦ , π₯π π denotes the mean of theThere wholeare population from measures which the sample was drawn while π₯ 3 common of central tendency. denotes the mean of the sample drawn from the population. MEAN: The ordinary average of the statistics, set of numbers. Because we are notarithmetic focusing much on inferential the difference between theseletβs two look things terribly important usmean. here. Before doing an example, at isnβt notation often used fortothe π₯ This is the standard mathematical symbol for the mean. It is pronounced βx barβ. π₯1 + π₯2 + β― + π₯π π₯π π₯= = π π MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency numbers π₯1For +any π₯2set + ofβ―π+ π₯π π₯π π₯1 , π₯2 , π₯3 β¦ , π₯π = π₯= π π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 (Round answer to 2 decimal places.) MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency numbers π₯1For +any π₯2set + ofβ―π+ π₯π π₯π π₯1 , π₯2 , π₯3 β¦ , π₯π = π₯= π π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 (Round answer to 2 decimal places.) π₯1 + π₯2 + β― + π₯π π₯= π MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency numbers π₯1For +any π₯2set + ofβ―π+ π₯π π₯π π₯1 , π₯2 , π₯3 β¦ , π₯π = π₯= π π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 (Round answer to 2 decimal places.) π₯1 + π₯2 + β― + π₯π π₯= π 3+3+8+3+1+5+8+8+8 π₯= 9 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency numbers π₯1For +any π₯2set + ofβ―π+ π₯π π₯π π₯1 , π₯2 , π₯3 β¦ , π₯π = π₯= π π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 (Round answer to 2 decimal places.) π₯1 + π₯2 + β― + π₯π π₯= π 3 + 3 + 8 + 3 + 1 + 5 + 8 + 8 + 8 47 π₯= = 9 9 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency numbers π₯1For +any π₯2set + ofβ―π+ π₯π π₯π π₯1 , π₯2 , π₯3 β¦ , π₯π = π₯= π π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. Example: Find the mean of 3 , 3 , 8 , 3 , 1 , 5 , 8 , 8 , 8 (Round answer to 2 decimal places.) π₯1 + π₯2 + β― + π₯π π₯= π 3 + 3 + 8 + 3 + 1 + 5 + 8 + 8 + 8 47 π₯= = = 5.22 9 9 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. This might be a good time to mention that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. MATH 110 14-2 Lecture: Statistics-Measures Central Tendency USING THE Sec CASIO fx-260 TO FIND THE MEAN OF AofSET OF NUMBERS 1. Press . (There are butπthis is one way to clear old data.) Forother anyways, set of numbers 2. Press . (Puts calculator tell if it is in stats π₯1 , π₯2in, π₯stats , π₯π 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention the Casio fx-260 calculator 5. After all data in, press . that Be careful! has a βstats modeβ that you can use to calculate means for you. Some people forget to press 6. You will find the mean in the calculator display. after the last number. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found on this summary sheet. USING THE CASIO fx-260 TO FIND THE MEAN OF A SET OF NUMBERS Forother anyways, set of numbers 1. Press . (There are butπthis is one way to clear old data.) π₯1 , π₯2in, π₯stats , π₯π 2. Press . (Puts calculator tell if it is in stats 3 β¦modeβ¦can by seeing βSDβ in the upper right corner of display.) There are 3mode common measures of central tendency. 3. Key in the first number and press . MEAN: arithmetic average ofafter the set numbers. 4. Key inThe eachordinary succeeding number, pressing eachofone. This might be a is good time to mention 5. After all data in, press . that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. 6. You will find the mean in the calculator display. Other useful tips β’Press to display how many numbers you have entered. β’ Once a number is entered, pressing enters it again. β’ These things and more can be found on this summary sheet. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. This might be a good time to mention that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency For any set of π numbers π₯1 , π₯2 , π₯3 β¦ , π₯π There are 3 common measures of central tendency. MEAN: The ordinary arithmetic average of the set of numbers. This might be a good time to mention that the Casio fx-260 calculator has a βstats modeβ that you can use to calculate means for you. You may be required to calculate a mean, median or mode from data presented in a frequency table. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mode of the data in the Score Frequency frequency table. 12 1 15 1 17 20 21 3 3 1 26 4 32 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mode of the data in the Score Frequency frequency table. 12 1 Because a frequency table already has 15 1 counts, finding the mode is easyβ¦ just find the score with the largest 17 3 frequency. 20 3 21 1 26 4 32 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mode of the data in the Score Frequency frequency table. 12 1 Because a frequency table already has 15 1 counts, finding the mode is easyβ¦ just find the score with the largest 17 3 frequency. 20 3 21 1 26 4 32 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mode of the data in the Score Frequency frequency table. 12 1 Because a frequency table already has 15 1 counts, finding the mode is easyβ¦ just find the score with the largest 17 3 frequency. 20 3 21 1 26 4 32 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mode of the data in the Score Frequency frequency table. 12 1 Because a frequency table already has 15 1 counts, finding the mode is easyβ¦ just find the score with the largest 17 3 frequency. 20 3 21 1 The mode is 26. 26 4 32 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 12 1 15 1 17 20 21 3 3 1 26 4 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 12 1 We need for the data to be in order to 15 1 find the median. Here the scores are already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 26 32 The mode is 26. 4 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 12 1 We need for the data to be in order to 15 1 find the median. Here the scores are already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 12 1 We need for the data to be in order to 15 1 find the median. Here the scores are already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 12 1 We need for the data to be in order to 15 1 find the median. Here the scores are already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency There is Find the median of the data in the Score one 12 Frequency frequency table. 12 1 We need for the data to be in order to 15 1 find the median. Here the scores are already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency There is Find the median of the data in the Score one 12 Frequency frequency table. one 1 12 1 We need for the data to be in order to 15 1 find the median. Here the scores are already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score ThereFrequency is frequency table. 1 12 one 15 1 We need for the data to be in order to 15 1 find the median. Here the scores are already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score ThereFrequency is frequency table. 1 12 one 15 1 We need for the data to be in order to two 2 15 1 find the median. Here the scores are already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 There We need for the data to be in order to 2 15 are three 1 find the median. Here the scores are 17βs. already in order BUT we have to be 17 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 There We need for the data to be in order to 2 15 are three 1 find the median. Here the scores are 17βs. already in order BUT we have to three be 17 3 3 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 There We need for the data to be in order to 2 15 are three 1 find the median. Here the scores are 17βs. already in order BUT we have to be four 17 3 4 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 There We need for the data to be in order to 2 15 are three 1 find the median. Here the scores are 17βs. already in order BUT we have to be five 17 3 5 careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 We need for the data to be in order to 2 15 There 1 find the median. Here the scores are already in order BUT we have to be 17 are three 3 5 20βs. careful because we do have to take 20 3 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 We need for the data to be in order to 2 15 There 1 find the median. Here the scores are already in order BUT we have to be 17 are three 3 5 20βs. careful because we do have to take 20 3 6 the frequencies into considerationsix when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 We need for the data to be in order to 2 15 There 1 find the median. Here the scores are already in order BUT we have to be 17 are three 3 5 20βs. careful because we do have to take seven 20 3 7 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 We need for the data to be in order to 2 15 There 1 find the median. Here the scores are already in order BUT we have to be 17 are three 3 5 20βs. careful because we do have to take eight 20 3 8 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 We need for the data to be in order to 2 15 There 1 find the median. Here the scores are already in order BUT we have to be 17 are three 3 5 20βs. careful because we do have to take eight 20 3 8 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX Letβs count down to the 8th score in the table. The 8th score in the table is 20. 32 The mode is 26. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the median of the data in the Score Frequency frequency table. 1 12 1 We need for the data to be in order to 2 15 There 1 find the median. Here the scores are already in order BUT we have to be 17 are three 3 5 20βs. careful because we do have to take eight 20 3 8 the frequencies into consideration when finding the middle value. 21 1 There are 15 scores 26 4 That means that the 8th score is the median. XXXXXXXXXXXXXXX 32 The mode is 26. Letβs count down to the 8th score in the table. The median is 20. The 8th score in the table is 20. 2 MATH Secas 14-2 Statistics-Measures of Central Tendency Note that110 as long theLecture: total number is not too large, wethe could just write outdata all the first. Score Find median of the in numbers the Frequency table. 12 15 17 17frequency 17 20 20 20 21 26 26 26 26 32 32 We need for the data to be in order to find the median. Here the scores are already in order BUT we have to be careful because we do have to take the frequencies into consideration when finding the middle value. There are 15 scores 12 15 1 1 17 20 21 3 3 1 26 4 32 The mode is 26. The median is 20. 2 MATH Secas 14-2 Statistics-Measures of Central Tendency Note that110 as long theLecture: total number is not too large, wethe could just write outdata all the first. Score Find median of the in numbers the Frequency table. 12 15 17 17frequency 17 20 20 20 21 26 26 26 26 32 32 We need for the data to be in order to find the median. Here the scores are already in order BUT we have to be careful because we do have to take the frequencies into consideration when finding the middle value. There are 15 scores 12 15 1 1 17 20 21 3 3 1 26 4 32 The mode is 26. The median is 20. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 15 1 17 20 21 3 3 1 26 4 32 The mode is 26. The median is 20. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 17 20 21 3 3 1 26 4 32 The mode is 26. The median is 20. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 17 3 20 3 21 1 26 32 The mode is 26. The median is 20. 4 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 17 3 20 3 21 1 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.old data.) 1. Press . (There are other ways, but this isThe onemedian way to clear MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 17 3 20 3 21 1 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS The median is 20. 2. Press . (Puts calculator in stats mode) MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 17 3 20 3 21 1 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS 3. Key in the first number and press . The median is 20. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 3 20 3 21 1 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 21 1 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 17 goes in 3 times 12 15 17 17 3 20 3 21 1 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 1 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 1 20 goes in 3 times 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 21 1 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 26 21 1 26 goes in 4 times 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 26 21 1 32 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 26 21 1 32 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each 32 goes in 2 times MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 26 21 1 32 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS is 20.one. 4. Key in each succeeding number, pressingThe median after each MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 26 21 1 32 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS The median is 20. 5. After all data is in, press . MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 26 21 1 32 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS The median is 20. 6. You will find the mean in the calculator display. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 26 21 1 32 26 4 32 2 TheOF mode is 26. USING THE CASIO fx-260 TO FIND THE MEAN A SET OF NUMBERS The median is 20. 6. You will find the mean in the calculator display. The mean is 21.8. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Find the mean of the data in the Score Frequency frequency table. 12 1 We will use the calculator stats mode. 15 1 KEYSTROKES 12 15 17 17 3 20 3 20 21 26 21 1 32 26 4 The mean is 21.8. 32 The mode is 26. The median is 20. 2 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary The median divides a dataset into two halves. MEDIAN X X X X X X X X X X X X X X X X MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary The median divides a dataset into two halves. The set of numbers below the median is called the lower half. MEDIAN X X X X X X X X X X X X X X X X MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary The median divides a dataset into two halves. The set of numbers below the median is called the lower half. The median of the lower half is called the first quartile (called π1 ). π1 MEDIAN X X X X X X X X X X X X X X X X MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary The median divides a dataset into two halves. The set of numbers below the median is called the lower half. The median of the lower half is called the first quartile (called π1 ). The set of numbers above the median is called the upper half. π1 MEDIAN X X X X X X X X X X X X X X X X MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary The median divides a dataset into two halves. The set of numbers below the median is called the lower half. The median of the lower half is called the first quartile (called π1 ). The set of numbers above the median is called the upper half. The median of the upper half is called the third quartile (called π3 ). π1 MEDIAN π3 X X X X X X X X X X X X X X X X MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary The median divides a dataset into two halves. The set of numbers below the median is called the lower half. The median of the lower half is called the first quartile (called π1 ). The set of numbers above the median is called the upper half. The median of the upper half is called the third quartile (called π3 ). With the minimum value and maximum value, we have the 5 numbers. MINIMUM π1 MEDIAN π3 X X X X X X X X X X X X X X X X MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number Summary The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary The median divides a dataset into two halves. The set of numbers below the median is called the lower half. The median of the lower half is called the first quartile (called π1 ). The set of numbers above the median is called the upper half. The median of the upper half is called the third quartile (called π3 ). With the minimum value and maximum value, we have the 5 numbers. MINIMUM π1 MEDIAN π3 MAXIMUM X X X X X X X X X X X X X X X X MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} The Five-Number Summary is a set of 5 numbers that, in some sense, describes or summarizes a dataset. DEFINITION: The Five-Number Summary The median divides a dataset into two halves. The set of numbers below the median is called the lower half. The median of the lower half is called the first quartile (called π1 ). The set of numbers above the median is called the upper half. The median of the upper half is called the third quartile (called π3 ). With the minimum value and maximum value, we have the 5 numbers. MINIMUM π1 MEDIAN π3 MAXIMUM X X X X X X X X X X X X X X X X MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MEDIAN MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MEDIAN MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 π1 MEDIAN MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 π1 MEDIAN MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 π1 MEDIAN π3 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. 60 + 61 = 60.5 2 LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency The Five-Number FIVE-NUMBER SUMMARY: {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Five-Number FIVE-NUMBER {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} We SUMMARY: often The represent the Five-Number Summary By a graph called a Box-and-Whisker Plot. This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Five-Number FIVE-NUMBER {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} We SUMMARY: often The represent the Five-Number Summary By a graph called a Box-and-Whisker Plot. This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. We LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN Draw a BOX from π1 to π3 π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Five-Number FIVE-NUMBER {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} We SUMMARY: often The represent the Five-Number Summary By a graph called a Box-and-Whisker Plot. This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. We LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM Extend WHISKERS from the box to min and max. FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } MATH 110 Sec 14-2 Lecture: Statistics-Measures of Central Tendency Five-Number FIVE-NUMBER {ππππππ’π ,Summary π1 , ππππππ , π3 , πππ₯πππ’π} We SUMMARY: often The represent the Five-Number Summary By a graph called a Box-and-Whisker Plot. This is a list of ages of presidents assuming office between 1901 and 1993. Construct the Five-Number Summary. We LOWER HALF UPPER HALF 42 43 46 51 51 51 52 54 55 55 56 56 60 61 61 64 69 MINIMUM π1 MEDIAN π3 MAXIMUM FIVE-NUMBER SUMMARY: { 42 , 51 , 55 , 60.5 , 69 } This presentation can be found at: http://cas.ua.edu/mtlc/UAMath110/LecNotes/Statistics/MATH110Sec14-2Lecture.pptx Some extra practice exercises can be found at: http://cas.ua.edu/mtlc/UAMath110/Exercises/Sec14-2Exercises.pdf (with step-by-step solutions at: http://cas.ua.edu/mtlc/UAMath110/Exercises/MATH110Sec14-2PracExercisesSOL.pptx)