§ 2.3 Goals (Procedure):
I Compute a central tendancy (mean, median, mode).
I Compute a weighted mean.
I Describe shapes of data sets.
§ 2.3 Goals (Non-procedure):
I Describe shapes of data sets.
I Find which type of central tendancy is suitable.
I Explore how different data sets respond to extreme values.
Assignment For June 2:
I Homework § 2.3: #61, 64, 65
Suggested Exercises: § 2.3: #6, 7, 8, 21, 23, 31, 41, 42, 57
Notes
The mean of a data set is the sum of the data entries divided by the number of entries.
Ex: The heights, in inches, of 2009 - 2010 Cleveland Cavaliers are listed:
74 78 81 87 81 80 77 80
85 78 80 83 75 81 73
What is the mean height?
a. Σ x = 1193 inches. b.
µ = 79 .
5 inches.
Notes
The median of a data set is the value that lies in the middle of the data when the data is ordered.
Ex: The ages of a sample of fans at a rock concert are listed:
24 27 19 21 18 23 21 20 19 33 30 29 21
18 24 26 38 19 35 34 33 30 21 27 30
What is the median age?
a. A stem-and-leaf plot is useful. b. 24 years old.
Notes

The mode of a data set is the data entry that occurs with the greatest frequency.
Ex: In a survey, 1000 U.S. adults were asked if they thought public mobile phone conversations were rude. 510 responded ”Yes,” 370 responded ”No,” and 120 responded ”Not sure.” What is the mode of the responses?
a. A Pareto chart is useful.
Notes
The weighted mean is the mean of a data set whose entries have varying weights.
Ex: Use the frequency distribution of the 50 wealthiest people in 2009 to find the weighted mean.
Class Frequency, f
35 - 41
42 - 48
49 - 55
56 - 62
2
5
7
7
1. Find a single number to use for each class.
63 - 69
70 - 76
10
5
2. Use the frequency f as the weights.
77 - 83
84 - 90
8
6
Notes
Notes

A consumer testing service obtained mileage (in miles per gallon) in five test runs with three types of cars.
Run 1 Run 2 Run 3 Run 4 Run 5
Car A : 28 32 28 30 34
Car B : 31
Car C : 29
29
32
31
28
29
32
31
30
The manufacturer of each car wants to advertise that its car performed best in this test. Which measure of central tendancy mean, median, or mode - should be used for its claim? Explain your reasoning for each car.
Notes
Which measure of central tendancy - mean, median, or mode - is allowed for each type of data - qualitative and quantitative?
Which measure of central tendancy - mean, median, or mode - should be used for each level of measurement of data - nominal, ordinal, interval, and ratio?
Notes
The U.S. exports (in billions of dollars) to 19 countries are listed:
9.1
12.5
12.9
15.5
22.0
22.2
24.9
27.9
28.8
28.9
32.3
34.7
39.7
53.6
54.5
65.1
69.7
151.2
261.1
1. Find the median and mean. Then find the mean and median by cutting out the entry of $261.1 billion dollars.
2. Which measure of central tendency was affected more by eliminating that value?
3. A 20th data entry of $17.7 billion dollars is added to the original data set. Which measure of central tendency was affected more by adding this value?
Notes