EXAMPLE 1 Making a Stem-and-Leaf Plot

Speeds of Animals

The table lists the maximum running speeds of various animals. How can the data be displayed to show the distribution of the speeds?

EXAMPLE 1

Speeds of Animals

A stem-and-leaf plot is a data display that helps you to see the way data are distributed. You can use a stem-and-leaf plot to place data in increasing order.

Making a Stem-and-Leaf Plot

EXAMPLE 1

Display the speeds of the animals in a stem-and-leaf plot.

SOLUTION

Write the stems first. Draw a vertical line segment next to the stems. Then record each speed by writing its ones’ digit on the same line as its corresponding tens’ digit.

Choose the stems and leaves. The numbers range from 32 to 70, so let the stems be the tens’ digits from 3 to 7. Let the leaves be the ones’ digits.

STEP 1

STEP 2

Making a Stem-and-Leaf Plot

EXAMPLE 1

Make an ordered stem-and-leaf plot. Include a key to show what the stems and leaves represent.

STEP 3

Unordered Plot Ordered Plot

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9 25 7 0 3

0

0

34567

2 90 3 5 7

0

0

Key: 4 7 = 47 Key: 4 7 = 47

Making a Stem-and-Leaf Plot

EXAMPLE 2 Interpreting a Stem-and-Leaf Plot

The point totals (rounded to the nearest tenth) for the 20 participants in a bicycle stunt competition are listed below. The rider with the greatest point total out of 100 points wins.

Bicycle Stunt Competition

89.4 90 87.5 84.3 89.7 90.3 91.1 91 86 84.1

89.2 86 89.1 88.2 89.5 85.6 90.5 90.2 91.1 88.9

Use a stem-and-leaf plot to order the data. Make a conclusion about the data.

EXAMPLE 2

SOLUTION

Begin by making an unordered stem-and-leaf plot. Because the point totals range from 84.1 to 91.4, the stems are the digits in the tens’ and ones’ places. The leaves are the digits in the tenths’ place.

Interpreting a Stem-and-Leaf Plot

EXAMPLE 2

SOLUTION

Then make an ordered stem-and-leaf plot.

8485868788899091

3 1

52 94 7 2 1 5

0 3 5 2 1 0 1

0 06

Key: 87 5 = 87.5

Unordered Plot8485868788899091

1 3

0 0

2 91 2 4 5 70 2 3 5 0 1 1

5

6

Key: 87 5 = 87.5

Ordered Plot

Interpreting a Stem-and-Leaf Plot

EXAMPLE 2

More than half of the participants finished near the top of the range, with 12 of the 20 participants having point totals greater than or equal to 89.

ANSWER

Interpreting a Stem-and-Leaf Plot

GUIDED PRACTICE for Examples 1 and 2

92 78 73 89 98 89 83 75 83 100

69 71 96 67 81 73 88 86 82 94

Test Scores

The test scores for the students in a social studies class are listed below. Make an ordered stem-and-leaf plot of the scores.

1.

GUIDED PRACTICE

ANSWER

for Examples 1 and 2

GUIDED PRACTICE

Use the stem-and-leaf plot from Exercise 1 to answer the questions.

2. How many test scores are greater than 84?

3. How many test scores are less than 80?

ANSWER 9

ANSWER 7

for Examples 1 and 2

GUIDED PRACTICE

4. Identify the median of the data?.

Use the stem-and-leaf plot from Exercise 1 to answer the questions.

ANSWER 83

5. How many modes do the data have? What are they?

ANSWER 3 modes; 73, 83, and 89

6. Make a conclusion about the test scores.

ANSWER Many scores fell in the 80’s, with two more scores below 80 than 90 or above. Most scores were above 70.

for Examples 1 and 2