Five-Minute Check (over Lesson 8–2)

Main Idea and Vocabulary

Example 1: Display Data in a Stem-and-Leaf Plot

Example 2: Describe Data

Example 3: Effect of Outliers

• stem-and-leaf plot

• leaf

• stem

• Display and analyze data in a stem-and-leaf plot.

Display Data in a Stem-and-Leaf Plot

BASEBALL The table below shows the number of home runs that Babe Ruth hit during his career from 1914 to 1935. Make a stem-and-leaf plot of the data.

Source: baberuth.com

Display Data in a Stem-and-Leaf Plot

Step 1 The digits in the least place value will form the leaves and the remaining digits will form the stems. In this data, 0 is the least value, and 60 is the greatest. So, the ones digit will form the leaves, and the tens digit will form the stems.

Step 2 List the stems 0 to 6 in order from least to greatest in the Stem column. Write the leaves, the ones digits of the home runs, to the right of the corresponding stems.

Step 3 Order the leaves and write a key that explains how to read the stems and leaves.

Display Data in a Stem-and-Leaf Plot

Answer:

A key shows how the

digits are related.

The ones digits of the

data form the leaves.

The tens digits of the

data form the stems.

1. A

2. B

3. C

4. D0% 0%0%0%

BUSINESS The table shows the number of hours spent aboard an airplane for a survey of business men and women. Make a stem-and-leaf plot of the data.

A. B.

C. D.

Describe Data

FITNESS The stem-and-leaf plot below shows the number of miles that Megan biked each day during July. Find the range, median, and mode of the data.

Describe Data

range: greatest distance – least distance = 30 – 5 or 25 miles

median: average of middle two values, or 12 miles

mode: most frequent value, or 10 miles

Answer: range: 25 miles; median: 12 miles; mode: 10 miles

1. A

2. B

3. C

4. D0% 0%0%0%

A. range: 25 inches; median: 10 inches; mode: 10 inches

B. range: 10 inches; median: 25 inches; mode: 15 inches

C. range: 25 inches; median: 14 inches; mode: 10 inches

D. range: 23 inches; median: 12 inches; mode: 10 inches

SNOWFALL The stem-and-leaf plot below shows the number of inches of snow that fell in Hightown during the month of January for the past 15 years. Find the range, median, and mode.

Effect of Outliers

ANIMALS The average life span of several animal species is shown in the stem-and-leaf plot. Which measure of central tendency is most affected by the inclusion of the outlier?

The mode, 20, is not affected by the inclusion of the outlier, 40.

Calculate the mean and median each without the outlier, 40. Then calculate them including the outlier and compare.

Effect of Outliers

Effect of Outliers

Answer: So, the median is most affected by the inclusion of the outlier.

The mean increased by 13.8 – 12.4, or 1.4, while the median increased by 15 – 13.5, or 1.5.

1. A

2. B

3. C

4. D0% 0%0%0%

TEST SCORES The test scores earned by a class of middle school math students on a chapter test are shown. What measure of central tendency is most affected by the inclusion of the outlier?

A. mean

B. median

C. mode

D. mean and median

End of the Lesson

Five-Minute Check (over Lesson 8–2)

Image Bank

Math Tools

Line Plots

1. A

2. B

3. C

4. D0% 0%0%0%

(over Lesson 8-2)

A. 15; 15.1; none

B. 15; 15.1; 15

C. 15; 15; 15.1

D. 15.1; 15; none

Find the mean, median, and mode for the set of data. Round to the nearest tenth if necessary.13, 17, 11, 12, 20, 14, 18, 16

1. A

2. B

3. C

4. D0% 0%0%0%

(over Lesson 8-2)

A. 38.7; 43; 41.5

B. 38.7; 41.5; 43

C. 43; 38.7; 41.5

D. 43; 41.5; 38.7

Find the mean median and mode for the set of data. Round to the nearest tenth if necessary. 14, 32, 35, 40, 37, 45, 48, 50, 43, 43

1. A

2. B

3. C

4. D0% 0%0%0%

(over Lesson 8-2)

A. 4; 6.3; 4

B. 6.3; 4; 6.3

C. 6.3; 4; 4

D. 4; 6.3; 6.3

Find the mean, median, and mode for the set of data. Round to the nearest tenth if necessary. 3, 1, 3, 5, 8, 4, 6, 4, 4, 2, 29

1. A

2. B

3. C

4. D0% 0%0%0%

(over Lesson 8-2)

A. Mean; because it is easier to find the average of the set of numbers and there are no big gaps in the middle of the data.

B. Median; because the data set has outliers and there are no big gaps in the middle of the data.

C. Mode; because the data has cluster and there are small gaps in the middle of the data.

D. Mean and median decribe the data best. The mode is too high.

Explain which measurement of central tendency best describes the data? 14, 32, 35, 40, 37, 45, 48, 50, 43, 43

1. A

2. B

3. C

4. D0% 0%0%0%

(over Lesson 8-2)

A. range

B. mode

C. median

D. mean

The average is another common term for which measurement of central tendency?

1. A

2. B

3. C

4. D0% 0%0%0%

(over Lesson 8-2)

A. 6

B. 7

C. 8

D. 9

If the Kentucky State University Orchestra has 42 musicians organized into 7 sections based on types of instruments, what is the mean number of musicians in each section?