Choosing Appropriate Measures Lesson Tutorials

Extension 10.3 Choosing Appropriate Measures Lesson Tutorials

You can use a measure of center and a measure of variation to describe the distribution of a data set. The shape of the distribution can help you choose which measures are the most appropriate to use.

Choosing Appropriate Measures Math The mean absolute deviation (MAD) uses the mean in its calculation. Practice So, when a data distribution is symmetric, Understand ● use the mean to describe the center and Quantities ● use the MAD to describe the variation. What effect can outliers have on The interquartile range (IQR) uses quartiles in its calculation. the mean? on the median? Explain. So, when a data distribution is skewed, ● use the median to describe the center and ● use the IQR to describe the variation.

EXAMPLE 1 Choosing Appropriate Measures

The dot plot shows the average number of hours students in a class sleep each night.

Amount of Sleep

Time (hours) 678910

a. What are the most appropriate measures to describe the center and the variation? Most of the data values are on the right clustered around 9, and the tail extends to the left. The distribution is skewed left. Data Displays In this extension, you will So, the median and the interquartile range are the most ● choose appropriate appropriate measures to describe the center and the variation. measures of center and variation to represent b. Describe the center and the variation of the data set. data sets. The median is 8.5 hours. The ﬁ rst quartile is 7.5, and the third quartile is 9. So, the interquartile range is 9 − 7.5 = 1.5 hours.

The data are centered around 8.5 hours. The middle half of the data varies by no more than 1.5 hours.

456 Chapter 10 Data Displays

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Bordering TheT frequency table shows the number of states that border Frequency States eache state in the United States. 0–1 3 a. Display the data in a histogram. Number of Bordering States 2–3 13 Draw and label the axes. Then for Each State in the U.S. 4–5 22 draw a bar to represent the 25 frequency of each interval. 20 6–7 10 15 8–9 2 10

Frequency 5 0

0–1 2–3 4–5 6–7 8–9 Number of bordering states

b. What are the most appropriate measures to describe the center and the variation? The left side of the graph is approximately a mirror image of the right side of the graph. The distribution is symmetric.

So, the mean and the mean absolute deviation are the most appropriate measures to describe the center and the variation.

Choose the most appropriate measures to describe the center and the variation. Find the measures you chose. 1. Prices of Jeans 2. Weekly Biking Times

Price Time (dollars) (hours) 28 30 3234 36 38 40 42 234567 8

3. REASONING Can you ﬁ nd the exact values of the mean and the mean absolute deviation for the data in Example 2? Explain.

4. GAS MILEAGE The frequency table shows the gas mileages Mileage Frequency of several vehicles made by a company. (miles per gallon) a. What are the most appropriate measures to describe 10–14 2 the center and the variation? 15–19 1 b. What conclusions can you make? 20–24 6 25–29 8 5. OPEN-ENDED Construct a dot plot for which the mean 30–34 10 is the most appropriate measure to describe the center 35–39 3 of the distribution.

Extension 10.3 Choosing Appropriate Measures 457

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