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Warm Up 11/16/15 Radical Product Property You can rewrite a radical as the product of two radical factors of its radicand ! a b ab ONLY when a≥0 and b≥0 For Example: 9 16 9 16 144 12 9 16 3 4 12 Equal Radical Quotient Property You can rewrite a radical as the quotient of the radical numerator of the radicand divided by the radical denominator of the radicand. a b a b ONLY when a≥0 and b>0 For Example: 64 16 64 16 64 16 4 2 8 4 2 Equal Rationalizing a Denominator The denominator of a fraction cannot contain a radical. To rationalize the denominator (rewriting a fraction so the bottom is a rational number) multiply by the same radical. Simplify the following expressions: 5 2 5 2 5 2 2 2 2 2 2 6 3 6 3 3 2 3 2 3 6 3 3 2 35 5 15 53 3 5 3 5 3 6 Warm Up 11/17/15 You can use the internet to help you find the answer! Interpret the stem and leaf Plot to the right to answer The question: The librarian at the public Library counted the number Of books on each shelf. How many shelves have at least 45 books but fewer than 65 Books? Books per shelf Stem Leaf 1 1127 2 48 3 46 4 45699 5 389 6 233 7 34456 Mean, Median, Mode and Range The Basics of Statistics Did You Know… That you probably use Statistics such as Mean, Median, Mode and Range almost every day without even realizing it?!? This week We Will Learn… • Mean • Median • Mode • Range • And how to use these in everyday life, as well as the classroom! What Do We Already Know? Sure, the words “Mean, Median, Mode and Range” all sound confusing… But what about the words we already know, like Average, Middle, Most Frequent, and Difference? They are all the same ideas! Mean • The mean is the Average of a group of numbers • It is helpful to know the mean because then you can see which numbers are above and below (in terms of value) the mean • It is very easy to find! Mean Example Here is an example test scores for Ms. Math’s class. 82 93 86 97 82 To find the Mean, first you must add up all of the numbers. 82+93+86+97+82=440 Now, since there are 5 test scores, we will next divide the sum by 5. 440÷5= 88 The Mean is 88! Now YOU try it!!! This is the Stat Family! Dad 34 Mom Katie 33 Jack Alex 5 5 1 Mean Here are the ages again… Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1 What is the Mean? Remember… Mean is the AVERAGE Try it on your paper and see what you come up with! Mean Remember, to find the mean, we have to first add up all of the numbers. 34+33+5+5+1= 78 Then, since there are 5 people in the family, we next divide by 5. 78÷5= 15.6 The Mean in this case is 15.6 Warm Up 11/18/15 • What is the mean of the following data set? • {105, 223, 458, 1,016, 557) Median • The Median is the middle value of a set of numbers. • The first step is always to put the numbers in order. Median Example • First, let’s examine these five test scores. 78 93 86 97 79 We need to put them in order. 78 79 86 93 97 The number in the middle is 86 78 79 86 93 97 In this case, the Median is 86! Median Example #2 Now, let’s try it with an even number of test scores. 92 86 94 83 72 88 First, we will put them in order 72 83 86 88 92 94 This time, there are two numbers in the middle, 86 and 88 72 83 86 88 92 94 Now we will need to find the Average/Mean of these two numbers, by adding them and dividing by two. 86+88= 174 174÷2= 87 Here the Median is 87 Median Here are the ages again… Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1 What is the Median? Remember… Median is the MIDDLE NUMBER Try it on your paper and see what you come up with! Median Remember, to find the mean, we have to first put all of the numbers in order. 34 33 5 5 1 The Mean in this case is 5 Warm Up 11/19/15 • What is the median of the following set of points scored in a game by Brian? • {12, 5, 31, 17, 14} Mode • The Mode refers to the number that occurs the most frequently of a set of numbers. • It’s easy to remember… the first two numbers are the same! MOde and MOst Frequently! Mode Example • Here is an list of temperatures for one week. Mon. Tues. Wed. Thurs. Fri. Sat. 77° 79° 83° 77° 83° 82° Sun. 77° Again, We will put them in order. 77° 77° 77° 79° 82° 83° 83° 77° is the most frequent number, so the mode= 77° Mode Here are the ages again… Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1 What is the Mode? Remember… Mode is the MOST FREQUENT Try it on your paper and see what you come up with! Mode Remember, to find the mode, we have to first put all of the numbers in order. 34 33 5 5 1 The Mode in this case is 5 Warm up 11/20/15 • What is the mode of the following set of test scores achieved by Steve? • {98, 97, 85, 84, 98, 97, 97} Range • The range is the difference between the highest and the lowest numbers of a set of numbers. • All we have to do is put the numbers in order and subtract! Range Example • Let’s look at the temperatures again. 77° 77° 77° 79° 82° 83° 83° The highest number is 83, and the lowest is 77. All you need to do is subtract! 83-77= 6 In this case, the Range is 6 Range Here are the ages again… Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1 What is the Range? Remember… Range is the DIFFERENCE Try it on your paper and see what you come up with! Range Remember, to find the range, we have to first put all of the numbers in order. 34 33 5 5 1 The highest age is 34, and the lowest is 1 Now we need to subtract to find the difference 34-1= 33 The range is 33