Measures of Central Tendency

1. Measures of Central Tendency

2. Range • The difference between the smallest and largest items of data. • Put the data in order. • Subtract the smallest number from the largest. To find the range of 7 test grades of 70, 70, 85, 94, 88 and 40 Put the data in order: 40, 70, 70, 85, 88, 94 Subtract: 94 – 40 = 54

3. Median • The middle number when the data is ordered from least to greatest. Data: 4, 7, 2, 3, 5 First reorder it: 2, 3, 4, 5, 7 Then find the middle # Memory Aide: Think of the median in the middle of some roads. Median is 4

4. Mode • The number(s) in a set of data that occurs the most often. Mode is 95 99, 95, 80, 85, 95, 90, 95 There can be more than one mode, or there can be no mode 99, 95, 80, 85, 94, 90, 97 No Mode Memory Aide: Most Often D E 85 & 95 are the modes 99, 95, 80, 85, 94, 85, 95

5. Mean • Same thing as average. • Add up all the data and divide by the number of items. To find the mean of 3 test grades of 70, 70, and 40 70 + 70 + 40 = 180 180 ÷ 3 = 60 Memory Aide: “Mean Old Average” I failed.

6. Outlier • Data that is a lot different than the other values, or is located far from the rest of the data. Memory Aide: An outlier is like an outfielder (far away from the others)

7. Look at the answer for the problem below. Did they correctly find the median and mode of the data set? Be prepared to discuss your answer.

8. Neither answer is correct. There are actually 2 modes & to find the median, the data must first be put in order from least to greatest. 33, 33, 35, 36, 36, 39, 43

9. Below is a list of the number of hours spent playing video games each week for 11 weeks. 3 2 2 3 3 3 19 2 3 3 1 What is the range? What is the mode? What is the median? Hint: Begin by putting the data in order.

10. 2 3 2 3 3 3 3 3 19 1 2 Range = 18 Mode = 3 Median = 3 Which measure of central tendency best describes the typical amount of time spent on the Internet?

11. Use the clock icons on the next slide to determine the average number of hours spent playing video games each week. • Each clock stands for 1 hour. Each row is a week. • Remember the average just means you want to spread out the data evenly. • So for this problem you want to evenly divide the hours (or clocks) over the 11 weeks (or rows). • Remember each row is a week. You cannot change the number of weeks (rows) or hours (clocks).

12. What is the mean?

13. Steps for finding mean mathematically: Add up all of the data. Count how many items of data you have. Divide your total amount by the number of items. 44 ÷ 11 = 4

14. Number of M&Ms in each bowl 3 4 6 3 14 m m m m m Create a diagram to illustrate this data. (Like we did with the clocks.) Rearrange your data to show the average. What is the mean? What is the outlier? Find the mean without the outlier. What effect does the outlier have on the mean if the outlier is greater than the mean? Hint: since there are 5 bowls, you should have 5 rows

15. Number of M&Ms in each bowl 3 4 6 3 14 m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m What is the mean? 6 What is the outlier? 14 Find the mean without the outlier. 4 What effect does the outlier have on the mean if the outlier is greater than the mean? Makes the mean larger

16. Number of M&Ms in each bowl 4 5 5 6 0 m m m m m Create a diagram to illustrate this data. (Like we did with the clocks.) Rearrange your data to show the average. What is the mean? What is the outlier? Find the mean without the outlier. What effect does the outlier have on the mean if the outlier is greater than the mean? Hint: since there are 5 bowls, you should have 5 rows

17. Number of M&Ms in each bowl 4 5 5 6 0 m m m m m m m m m m m m m m m m m m m m m m m m m What is the mean? 4 What is the outlier? 0 Find the mean without the outlier. 5 What effect does the outlier have on the mean if the outlier is greater than the mean? Makes the mean smaller