1. Measures of Central Tendency
Dr. Fowler  AFM  Unit 8-2
Measures of Central Tendency
Compute the mean, median, and mode of distributions.
Find the five-number summary of a distribution with the Box and Whisker Plot.

2. The Mean:
We use the Greek letter Σ (capital sigma) to indicate a sum. For example, we will write the sum of the data values 7, 2, 9, 4, and 10 by Σx =
We represent the mean of a sample of a population by x (read as “x bar”), and we will use the Greek letter μ (lowercase mu) to represent the mean of the whole population.

3. The Mean: Example: Listed are the yearly earnings of some celebrities.
What is the mean of the earnings of the celebrities on this list?
Is this mean an accurate measure of the “average” earnings for these celebrities?
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4. The Mean:
Solution (a): Summing the salaries and dividing by 10 gives us
Solution (b): Eight of the celebrities have earnings below the mean, whereas only two have earnings above the mean. The mean in this example does not give an accurate sense of what is “average” in this set of data because it was unduly influenced by higher earnings.

5. What is the Median?
Arrange the numbers in ascending order (smallest to greatest).
The median is the middle number. If there are 2 middle numbers, then the median is the average of the 2 middle numbers.

6. What is the Median of the celebrity salaries?
Arrange in ascending order: 20, 30, 32, 33, 33, 40, 45, 45, 110, 260
2) The median is the middle number. Since there are 2 middle numbers, we add them and divide by 2: = 73 divide by 2 = 36.5 million

7. The Mode:

8. The Mode: Example: Find the mode for each data set.
a) The mode is 5.
b) 3, 3, 3, 2, 1, 4, 4, 9, 9, 9
b) 2 modes: 3 and 9.
c) 98, 99, 100, 101, 102
c) no mode.
d) 2, 3, 4, 2, 3, 4, 5
d) no mode.

9. The Five Number Summary

10. The Five Number Summary
Example: Consider the list of ages of some of the past U.S. Presidents at inauguration:
42, 43, 46, 51, 51, 51, 52, 54, 55,
55, 56, 56, 60, 61, 61, 64, 69.
Find the following for this data set:
a) the lower and upper halves
b) the first and third quartiles
c) the five-number summary
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11. The Five Number Summary
Solution:
(a): Finding the median, we can identify the lower and upper halves.
(b): The median of the lower half is
The median of the upper half is
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12. The Five Number Summary
(c): The five number summary is
We represent the five-number summary by a graph called a box-and-whisker plot.
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13. Box & Whisker on TI-84 https://www.youtube.com/watch?v=iobQ-ge26kU
Section 15.2, Slide 13

14. Excellent Job !!! Well Done