copyright © 2011 pearson education, inc. putting statistics to work

Copyright © 2011 Pearson Education, Inc.

Putting Statistics to Work

Copyright © 2011 Pearson Education, Inc.

Slide 6-3

Unit 6A

Characterizing Data

6-A

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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

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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

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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

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Slide 6-12

Two single-peaked (unimodal) distributions

A double-peaked (bimodal) distribution

Shapes of Distributions

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Slide 6-13

Symmetry

A distribution is symmetric if its left half is a mirror image of its right half.

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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

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Assignment

P. 379-380 7-37 odd

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