1. Mean, Median, Mode and Range

2. Measures of Central Tendency
Measure of central tendency – A value that represents the centre of a data set, can be the mean, median or mode.
Data Set – A collection of numbers
Ex: [9,13,12,8,8] is a data set

3. Mean
The “mean” is computed by adding all of the numbers in the data together and dividing by the number of elements contained in the data set.
Example:
Data Set = 2, 5, 9, 3, 5, 4, 7
Number of Elements in Data Set =
Mean =

4. Median
The “median” of the data set depends on whether the number of elements in the data set is odd or even. Steps to find the median:
Reorder the data set from smallest to largest.
If the number of elements is odd the median is the middle number.
If the number of elements is even the median is the average of the two middle numbers.

5. Median Example #1: Example #2: Find the median of the data set:
9,13,12,8,8
Written in increasing order =
8, 8, 9, 12, 13
Median = 9
Example #2:
Find the median of the data set:
6,2,7,19,13, 9
Written in increasing order =
2, 6, 7, 9, 13, 19
Median =
(7+9) ÷ 2 = 8

6. Mode
The mode for a data set is the element that occurs the most often. It is not uncommon for a data set to have more than one mode. Some sets have no mode.
Example #1:
[9,13,12,8,8]
Mode = 8
Example #2:
[6,2,7,19,13, 9]
Mode = no mode
Example #3:
[2,2,6,8,7,9,8]
Mode = 2 and 8

7. Range
The range for a data set is the difference between the largest value and the smallest value of a data set.
Example #1:
[9,13,12,8,8]
13 – 8 = 5
Example #2:
[6,2,7,19,13, 9]
19 – 2 = 17
Example #3:
[2,2,6,8,7,9,8]
9 – 2 = 7

8. Common Errors
Not arranging the data in ascending order prior to determining the median.
The median in an even-numbered data set is not both middle numbers, but the average of the two.
When no mode exists, the mode is not 0.

9. Which measure of central tendency should I use?
Advantage
Disadvantage
Mean
Commonly used
Easy to calculate
Useful when comparing
Skewed by extreme values
Median
Extreme values do not affect the median
Difficult to arrange large sets of data in order
Mode
Extreme values do not affect the mode
Useful when data values are limited.
Unless there is only one mode the results can be difficult to make sense of.

10. Example
The weekly salaries of six employees at McDonald’s are $140, $220, $90, $180, $140, $200. For these six salaries find the mean, median and mode.
List the data in order: 90, 140, 140, 180, 200, 220
Mean: = $161.67
Median: 90,140,140,180,200,220
The two numbers that fall in the middle need to be
averaged. ( ) / 2 = 160
Mode: The number that appears the most is 140

11. Example
Andy has grades of 84, 65 and 76 on three math tests. What would his score be on the next test if his average is exactly 80 on the four tests?
Andy will need a 95% on his next test.
(4) (80) = x
320 = x
320 – 225 = x
95 = x

12. Example
Test scores for a class of twenty students are 93, 84, 97, 98, 100, 78, 86, 100, 85, 92, 72, 55, 91, 90, 75, 94, 83, 60, 81, 95. Find the mean, median and mode of the data set.
Mean: 20
= 1709
= 85.5

13. Example
Test scores for a class of twenty students are 93, 84, 97, 98, 100, 78, 86, 100, 85, 92, 72, 55, 91, 90, 75, 94, 83, 60, 81, 95. Find the mean, median and mode of the data set.
Median:
Order data:
55, 60, 72, 75, 78, 81, 83, 84, 85, 86, 90, 91, 92, 93, 94, 95, 97, 98, 100, 100
Find the average of the two middle numbers. 2
= 176
= 88

14. Example
Test scores for a class of twenty students are 93, 84, 97, 98, 100, 78, 86, 100, 85, 92, 72, 55, 91, 90, 75, 94, 83, 60, 81, 95. Find the mean, median, mode, and range of the data set.
Mode:
55, 60, 72, 75, 78, 81, 83, 84, 85, 86, 90, 91, 92, 93, 94, 95, 97, 98, 100, 100
The mode is 100.
Range:
Largest value = Smallest value = 55
Range = Largest value – Smallest value
Range = 100 – 55
Range = 45

15. Example

16. Example

17. Example

18. Example

19. Example
A store owner keep a tally of the sizes of suits purchased in her store. Which measure of central tendency should the storeowner use to describe the average size suit sold?
Mean
A tally was made of the number of times each color of crayon was used by a kindergarten class. Which measure of central tendency should the teacher use to determine which color is the favorite color of her class?
Mode

20. Example
A tally was made of the number of times each color of crayon was used by a kindergarten class. Which measure of central tendency should the teacher use to determine which color is the favorite color of her class?
The favorite color would be the color appearing the most number of times. Use the mode.

21. Example
You are ordering bowling shoes for a bowling alley. Which measure of central tendency would most helpful in this situation?
Mode
You want to know if you read more or fewer books per month than most people in your class. Which measure of central tendency would most helpful in this situation?
Median
You want to know the “average” amount spent per week on junk food in your class. Which measure of central tendency would most helpful in this situation?
Mean

22. Portfolio Work Mode pg 68-69 #1,2(B),3,4,5,6
Median pg (A,C)2,3(B,C),
Mean pg #1,3,4
Mini-task