2. Mini Lecture: Mode, Median, Mean The 411 for a successful data analysis.

3. THE MODE The most common number The most frequently occurring number

4. THE MODE In a bar graph, the mode is the highest bar. In a line plot, the mode is the highest column.

5. THE MODE It is possible to have more than one mode. This occurs if there is a tie.

6. EXAMPLE DATA SET 3, 8, 9, 12, 3, 10, 15, 9 In this example, the mode is 3 and 9 because both occur the most times. (twice)

7. THE MODE It is possible to have no mode. This occurs when all of the data entries occur the same number of times.

8. THE MODE EXAMPLE DATA SET 4, 7, 2, 9, 12, 3 All of the numbers occur one time, so there is no mode.

9. THE MEDIAN This is the middle number. Half of the data entries are higher than the median. Half of the data entries are lower than this number.

10. THE MEDIAN Before attempting to determine the median, you must put the data entries in numerical order!

11. THE MEDIAN I REPEAT, YOU MUST PUT THE ENTRIES IN NUMERICAL ORDER!!

12. THE MEDIAN To find the median: Simply mark off a number from each end of the data set until you are left with one number remaining. This is to insure you have marked off the same amount of numbers above and below the median.

13. THE MEDIAN BUT WAIT... TROUBLE LIES AHEAD... If the number of data entries is EVEN, you will mark off all of the numbers.

14. THE MEDIAN The Solution: 1.Mark off the entries as before, but stop when there are two numbers remaining. 2.Find the halfway point between the two numbers - the mean.

15. THE MEDIAN EXAMPLE DATA SET 8, 3, 9, 12, 4, 4, 6, 10, 5 The median is 6. Did you remember to put the entries in numerical order?

16. THE MEDIAN 3, 4, 5, 6, 8, 9, 10, 12 Notice that there are four entries higher than 6 and four entries lower than 6.

17. THE MEDIAN One More Example… 8, 3, 9, 12, 4, 4, 6, 10, 5, 11 After putting the numbers in order, one gets… 3, 4, 4, 5, 6, 8, 9, 10, 11, 12

18. THE MEDIAN This time there are two middle numbers - 6 and 8. The median is the halfway point between these two numbers.... 7 !!!!

19. THE MEAN This number represents fairness.

20. THE MEAN If you collected all of the data, golf balls in this case, put them in a big pile, and then made sure everyone received the same amount; this amount would be the mean.

21. But you don’t have that many golf balls, and you don’t want to have to do that every time. So, there is an easier way…

22. THE MEAN 1.Add all of the entries in the data set. 2.Take that sum and divide by the number of entries in the data set. P.S. It is okay to get decimal numbers.

23. THE MEAN EXAMPLE DATA SET 8, 3, 9, 11, 4, 12, 6, 10, 7, 5 The mean is 7.5.

24. THE MEAN 1.The sum of the data set is 75. 2.There are 10 entries. 75 / 10 = 7.5