Main Idea and New Vocabulary

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

Example 2: Analyze Stem-and-Leaf Plots

Example 3: Effect of Outliers

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

• stem-and-leaf plot

• leaf

• stem

• outlier

Display Data in a Stem-and-Leaf Plot

SPORTS The table shows the number of home runs Cliff Floyd hit in the seasons from 1993 to 2008. Display the data in the table in a stem-and-leaf plot.

Step 1 Choose the stems using digits in the tens place, 0, 1, and 2. The least value, 1, has 0 in the tens place. The greatest value, 34, has 3 in the tens place.

Display Data in a Stem-and-Leaf Plot

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

Display Data in a Stem-and-Leaf Plot

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

Display Data in a Stem-and-Leaf Plot

Display Data in a Stem-and-Leaf Plot

The ten digits of the data form the stem.

The ones digits of the data form the leaves.

Always write each leaf, even if it repeats.

Include a key.

Display Data in a Stem-and-Leaf Plot

Answer:

TENNIS The table shows the number of service aces Joe hit in tennis matches each week of the tennis season. Display the data in the table in a stem-and-leaf plot.

A.

B.

C.

D.

FOOTBALL The stem-and-leaf plot shows the number of points scored by the University of Florida football team in the 2007 season. Find the range, median, and mode of the data.

Analyze Stem-and-Leaf Plots

range: most points – least points= 59 – 17 or 42

median: middle value, 45

mode: most frequent value, 59

Analyze Stem-and-Leaf Plots

Answer: The range is 42, the median is 45, and themode is 59.

A. range: 17; median: 15; mode: 21

B. range: 8; median: 15; mode: 21

C. range: 17; median: 5; mode: 1

D. range: 8; median: 5; mode: 1

VOLLEYBALL The stem-and-leaf plot shows the number of matches won over the last 10 seasons by a high school volleyball team. Find the range, median, and mode of the data.

Effect of Outliers

BASKETBALL The stem-and-leaf plot shows the number of points scored by a high school basketball player. Which measure of central tendency is most affected by the outlier?

The modes, 15 and 31, are not affected by the inclusion of the outlier, 49.

Calculate the mean and median, each without the outlier, 49. Then calculate them including the outlier and compare.

Effect of Outliers

20

without the outlier

Effect of Outliers

Answer: The mean increased by 21.9 – 19.7, or 2.2, while the median increased by 20 – 19 or 1. Since 2.2 > 1, the mean score is most affected.

with the outlier

A. median

B. mode

C. mean

D. The outlier does not affect any of the measures.

BIRD-WATCHING The stem-and-leaf plot shows the number of birds in Lucy’s backyard over 8 days. Which measure of central tendency is most affected by the outlier?