This document discusses three measures of central tendency: mean, median, and mode. It provides examples and step-by-step explanations for calculating each measure. The mean is the average and is calculated by adding all values and dividing by the number of values. The median is the middle number when values are ordered from least to greatest. The mode is the value that occurs most frequently in a data set.

1. Measures of central tendencyDominique Warmsley& Bettina BonsuMarch 29, 2010Math 300-003

2. When you hear someone use the word “average” to describe a set of numbers, there are 3 ways you can describe data, all of which can be thought of as “measures of central tendency” 1. Mean 2. Median 3. Mode

3. Mean: A set of numbers is the sum of values divided by the number of values. We can write this as a formula.Example: These are the values 5 + 10 + 7+ 12 + 8 + 6= 48 Add all the numbersThen count all the values and then divide by number ofvalues. 48 divided by 6 = 8So the mean for this set of values is 8

4. Work It out!What is the Mean of this set 7,10, 8, 14, 6Remember: follow all the steps!

5. Answer is:7 + 10 + 8 + 14+ 6= 4545 divided by 5 is ……… 9So your mean is 9

6. Median: a middle number of a set of numbers. You have to make sure your numbers are in order first.Values need to be ordered least to greatest.If the number of data values in the list is odd, thenthe median is the middle number in the list.If the number of data value is even, there is no single middlenumber . So the median is the mean of the 2 middle numbers in the list.

7. Watch Me!!!Example: 35, 74, 53, 98, 32, Place in order least to greatest32, 35, 53, 74, 98 The median is 53There are 5 values (an odd #), so the median is the middle number.

8. Now I’ll watch you!4200, 3600, 4500, 3500, 3800Now put them in order, and find your median

9. See it wasn’t that hardThe order least to greatest3500, 3600, 3800, 4200, 4500Because there are five data values (an odd number) the middle number ismedian. 3800 is the median. But you knew that right.

10. It can also look like this …..2600, 3900, 9800, 2200, 4100, 1500Next step is least to greatest1500, 2200, 2600, 3900, 4100, 9800The middle # are….. 2600, 3900you add both numbers 2600 + 3900 = 6500 Then 6500 divided by 2 = 3250Remember these steps…….

11. Now you can try this …..Find the median of this value set:26.08, 39.02, 98.07, 22.03, 41.04, 15.02

12. Solution…..Find the median of this value set:26.08, 39.02, 98.07, 22.03, 41.04, 15.02 In order from smallest to largest:15.02, 22.03, 26.08, 39.02, 41.04 ,98.07 Taking the mean of the middle two values 26.08 + 39.02= 65.1 65.1 divided by 2= 32.55

13. Mode: set of a value that occur most often. If two values occur most often we say the data is a bimodal.If more than two values occur most often, we say there is no mode.

14. Data SetsExample1:6.3, 12.5, 2.3, 6.3, 1.2, 3.3, 6.3,The data value 6.3 appears more often then any number . Therefore 6.3 is the mode.Example 2:2, 12, 14, 67, 98, 6, 15, 13, 10 No data value occurs most often, There isno mode for this set.

15. Now you can try this …..Find the mode of the value sets :Pink, blue, silver, yellow, pink , blue , pink6, 14, 13, 12, 14, 6, 5, 6, 10, 14, 22, 5, 10, 3, 6, 19, 11, 20, 19

16. Solution……Find the mode of the value sets :Pink, blue, silver, yellow, pink , blue , pink Mode is: pink6, 14, 13, 12, 14, 6, 5, 6, 10, 14, 2Bimodal sets are: 6, 142, 5, 10, 3, 6, 9, 11, 20, 19Mode is: none

17. Food For Thought!So, remember when you think average,think a set a numbers . And revisit your friends :Mean Median Mode Remember math is your friend ! Give him a hug