Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript

Working with Data Average 3 Averages There are 3 types of average (central tendency) • Mean • Mode • Median Average is a way of comparing data. SLO: To understand what is Mean Average Mean is found by spreading out the numbers evenly 2, 5, 2, 1, 5 How many beads would be in each pile if each of the 5 piles had the same number of beads? Mean average = 3 (3 in each pile) A quicker way….. To even out columns of numbers could take a long time. Here is a quicker method that does not involve beads. SLO: To calculate the mean average Sum (you will need to know this word) Sum – the answer to an addition problem. Copy into your notes To Find the Mean Average • Step 1 – Add all the numbers. 2 + 5 + 2 + 5 + 1 = 15 1 2 3 4 5 Step 2 – Divide the sum by the number of numbers. 15 ÷ 5 = 3 Mean average = 3 ?5 Your Turn: What is the mean of these numbers? 7, 10, 16 33 ÷ 3 = 11 Your Turn: What is the mean of these numbers? 2, 9, 5, 4 5 Your Turn: What is the mean of these numbers? 1, 2, 7, 11, 9 6 Your Turn: What is the mean of these numbers? 4, 3, 1, 3, 2, 7, 1 3 Web resource http://www.youtube.com/watch?v=UVnelMfhtrg Youtube video how to find mean average (Very strange man!) SLO: To find the Median Average Copy into your notes Definition Median is in the Middle (List must be in order) Copy into your notes Median Example #1 Find the median of these five test scores. 10 1 6 3 5 Step 1: Put them in order. 1 3 5 6 10 Step 2: Find the middle number 1 3 5 6 10 The Median is 5 Your Turn: Find the Median of the following 21, 18, 24, 19, 27 Step 1 – Arrange the numbers in order from least to greatest. 18, 19, 21, 24, 27 Step 2 – Find the middle number. 21 is your median number. Copy into your notes Median Example #2 Find the median of an even number of test scores. 92 86 94 83 72 88 Step 1: put them in order 72 83 86 88 92 94 Step 2: There are two numbers in the middle, 86 and 88 72 83 86 88 92 94 Step 3: Find half way between these two numbers, by adding them and dividing by two. 86+88= 174 174÷2= 87 The Median is 87 Your Turn: Find the Median of the following 21, 25, 19, 28, 27, 18 Step 1 – Arrange the numbers in order from least to greatest. 18, 19, 21, 25, 27, 28 Step 2 – Find the middle number. Step 3 – As there are two middle numbers, find the middle of these two numbers. (46 ÷ 2) 23 is your median number. Your Turn: What is the median of these numbers? 16, 10, 7 7, 10, 16 10 Your Turn: What is the median of these numbers? 29, 8, 4, 11, 19 4, 8, 11, 19, 29 11 Your Turn: What is the median of these numbers? 31, 7, 2, 12, 14, 19 2, 7, 12, 14, 19, 31 13 12 + 14 = 26 2) 26 Your Turn: What is the median of these numbers? 53, 5, 81, 67, 25, 78 5, 25, 53, 67, 78, 81 60 53 + 67 = 120 2) 120 Web resources http://www.youtube.com/watch?v=loAAovIKLGw (youtube video to find median) SLO: To find the mode average Copy into your notes Definition Mode is the most Popular A little French…. • A la mode – the most popular or that which is in fashion. Baseball caps are a la mode today. Copy into your notes Example 1 In a set of numbers the Mode is the number that appears most often. 1, 1, 3, 7, 10, 13 Mode = 1 Copy into your notes Example 2 1, 1, 1, 3, 7, 7, 7, 10, 10, 13 There are 2 numbers to choose from so there are 2 modes (bimodal) Mode = 1 and 7 Your Turn: Find the mode 21, 18, 24, 19, 18 Mode = 18 Your Turn: Which number is the mode? 29, 8, 4, 8, 19, 4 Mode = 4 and 8 Your Turn: Which number is the mode? 1, 2, 2, 9, 9, 4, 9, 10 Mode = 9 Your Turn: Which number is the mode? 22, 21, 27, 31, 21, 32 Mode = 21 Your Turn: Here is an list of temperatures for one week. Find the mode temperature. Mon. Tues. Wed. Thurs. Fri. Sat. Sun. 77° 79° 83° 77° 83° 77° 82° 77° is the most frequent number, so the mode= 77° Your Turn: Which number is the mode? 6, 8, 3, 8, 5, 4, 3, 9, 6 Mode = 3, 6 and 8 (Tri-modal) Web Resources http://www.youtube.com/watch?v=dam-TCRbkFw (youtube clip to find mode average, deals with multiple modes) Spread Spread Average looks at how data is grouped. Spread looks at the distribution of the data. SLO: To find the range of a set of data Difference A word you will need to know Difference – the answer to one number subtracted from another. E.g. the difference between 8 and 3 is 5 Definition Range is the difference between the highest and lowest Copy into your notes To find the range we subtract the lowest value in the set from the highest value. Range = highest value – lowest value When the range is small; the values are similar in size. When the range is large; the values vary widely in size. Copy into your notes: E.g. Find the Range of 21, 18, 24, 19, 27 Step 1: Find the lowest and highest numbers. Step 2: Find the difference between these 2 numbers. 27 – 18 = 9 The range is 9 Your Turn: Find the Range • Find the range from the temperatures. 77° 77° 77° 79° 82° 83° 83° The highest number is 83, and the lowest is 77. 83-77= 6 The Range is 6 Your Turn: Find the Range 1, 1, 3, 7, 10, 13 Range = 13 – 1 = 12 What is the range? 29, 8, 4, 8, 19 29 – 4 = 25 What is the range? 22, 21, 27, 31, 21, 32 32 – 21 = 11 What is the range? 31, 8, 3, 11, 19 31 – 3 = 28 What is the range? 23, 7, 9, 41, 19 41 – 7 = 34 SLO: Not to mix up mean, median, mode and range In conclusion Average: Mean (sum ÷ #) Mode (most) Median (Middle) Spread Range (Biggest – Smallest) Your Turn: find the Mean Dad Mum 34 33 Jack Alex Katie 5 5 1 The Mean 34+33+5+5+1= 80 Then, since there are 6 people in the family, we next divide by 6. 78÷6= 13 Your Turn: Find the Median Dad Mum 34 33 Jack Alex Katie 5 5 1 The Median first put all of the numbers in order. 34 33 5 5 1 The Mean in this case is 5 Mode Dad Mum 34 33 Jack Alex Katie 5 5 1 The Mode See which number appears the most 34 33 5 5 1 The Mode in this case is 5 Your Turn: find the Range Dad Mum 34 33 Jack Alex Katie 5 5 1 The Range 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 Web resources http://www.bbc.co.uk/bitesize/ks2/maths/data/mode_median_mean_range/play/ (individual game for mean, median and mode) http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/measuresofaverageact.shtml (Notes and individual interactive mean, median and mode questions) http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.STAT&ID2=AB.MATH.JR.STA T.CENT&lesson=html/object_interactives/central_tendency/use_it.html (mean, mode, median game) http://www.youtube.com/watch?v=oNdVynH6hcY (Mean, median and mode song) http://www.bbc.co.uk/bitesize/ks2/maths/data/mode_median_mean_range/quiz/q10083371/ (mean, mode, median, range quiz) Extension: Potential Problem with Means Median Mean Median Mean Problems with Mode • May not exist • May not be unique – E.g. “bi-modal” distribution • Two values occur with same frequency Thanks This power point has been put together using power points, images, videos and games from the net. Thank you to all those who have placed their work in the public domain. For others to use.