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Copyright © 2011 Pearson Education, Inc.
Putting Statistics to Work
Copyright © 2011 Pearson Education, Inc.
Slide 6-3
Unit 6A
Characterizing Data
6-A
Copyright © 2011 Pearson Education, Inc.
Slide 6-4
The distribution of a variable (or data set) describes the values taken on by the variable and the frequency (or relative frequency) of these values.
Definition
6-A
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Slide 6-5
The mean is what we most commonly call the average value. It is defined as follows:
The median is the middle value in the sorted data set (or halfway between the two middle values if the number of values is even).
The mode is the most common value (or group of values) in a distribution.
Measures of Center in a Distribution
6-A
Copyright © 2011 Pearson Education, Inc.
You try it!
Slide 6-6
The lengths (in minutes) of a sample of cell phone calls are shown:
6 19 3 6 12 8
Find the mean.
A. 54
B. 9
C. 6
D. 7
6-A
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Slide 6-7
Mean vs. Average
6-A
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Slide 6-8
6.72 3.46 3.60 6.44 26.70 (data set)
3.46 3.60 6.44 6.72 26.70 (sorted list)
(odd number of values)
median is 6.44exact middle
Example: Find the median of the data set below.
Finding the Median for anOdd Number of Values
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Slide 6-9
6.72 3.46 3.60 6.44 (data set)
3.46 3.60 6.44 6.72 (sorted list)
(even number of values)
3.60 + 6.44
2median is 5.02
Example: Find the median of the data set below.
Finding the Median for anEven Number of Values
6-A
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Slide 6-10
Finding the Mode
a. 5 5 5 3 1 5 1 4 3 5
b. 1 2 2 2 3 4 5 6 6 6 7 9
c. 1 2 3 6 7 8 9 10
Mode is 5
Bimodal (2 and 6)
No Mode
Example: Find the mode of each data set below.
6-A
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Slide 6-11
Effects of OutliersAn outlier is a data value that is much higher or much lower than almost all other values.
Consider the following data set of contract offers:
$0 $0 $0 $0 $2,500,000
The mean contract offer is
As displayed, outliers can pull the mean upward (or downward). The median and mode of the data are not affected.
000,500$5
000,500,2$0$0$0$0$
mean
6-A
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Slide 6-12
Two single-peaked (unimodal) distributions
A double-peaked (bimodal) distribution
Shapes of Distributions
6-A
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Slide 6-13
Symmetry
A distribution is symmetric if its left half is a mirror image of its right half.
6-A
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Slide 6-14
A distribution is left-skewed if its values are more spread out on the left side.
A distribution is right-skewed if its values are more spread out on the right side.
Skewness
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Slide 6-15
Variation
From left to right, these three distributions have increasing variation.
Variation describes how widely data values are spread out about the center of a distribution.
6-A
Copyright © 2011 Pearson Education, Inc.
Assignment
P. 379-380 7-37 odd
Slide 6-16
