Stem-and-Leaf Plots and Box Plots Worksheet

Question 1

Create a stem-and-leaf plot for these quiz scores: 72, 85, 91, 76, 88, 84, 90, 73, 79, 86. Use the tens digit as the stem.

Accepted Answer

The stem-and-leaf plot is: Stem 7 has leaves 2, 3, 6, 9; Stem 8 has leaves 4, 5, 6, 8; Stem 9 has leaves 0, 1. A correct key is 7 | 2 = 72.

Question 2

Use this stem-and-leaf plot: Stem 4: leaves 1, 5, 8; Stem 5: leaves 0, 2, 2, 9; Stem 6: leaves 3, 7. Key: 4 | 1 = 41. How many data values are in the plot?

Accepted Answer

There are 9 data values in the plot because there are 9 leaves total.

Question 3

Use this stem-and-leaf plot: Stem 2: leaves 4, 6, 9; Stem 3: leaves 1, 5, 8; Stem 4: leaves 0, 2. Key: 2 | 4 = 24. What is the median of the data?

Accepted Answer

The data values are 24, 26, 29, 31, 35, 38, 40, and 42. The median is 33 because it is the average of the 4th and 5th values, 31 and 35.

Question 4

A data set is shown in a stem-and-leaf plot: Stem 1: leaves 2, 5, 7; Stem 2: leaves 0, 4, 6, 8; Stem 3: leaves 1, 3. Key: 1 | 2 = 12. What is the range of the data?

Accepted Answer

The range is 21 because the greatest value is 33 and the least value is 12, and 33 - 12 = 21.

Question 5

The numbers of books read by students are 4, 7, 9, 10, 12, 13, 15, 18, 20, 22, and 25. Find the five-number summary.

Accepted Answer

The five-number summary is minimum 4, first quartile 9, median 13, third quartile 20, and maximum 25.

Question 6

Make a box plot from this five-number summary: minimum 12, first quartile 18, median 24, third quartile 30, maximum 36.

Accepted Answer

The box plot should have whiskers at 12 and 36, a box from 18 to 30, and a median line at 24.

Question 7

A box plot has a minimum of 15, first quartile of 22, median of 28, third quartile of 35, and maximum of 41. What is the interquartile range?

Accepted Answer

The interquartile range is 13 because 35 - 22 = 13.

Question 8

A box plot shows test times in minutes. The minimum is 20, Q1 is 30, the median is 42, Q3 is 50, and the maximum is 60. What percent of the test times are between 30 and 50 minutes?

Accepted Answer

About 50 percent of the test times are between 30 and 50 minutes because the box from Q1 to Q3 contains the middle half of the data.

Question 9

Class A has a median score of 78 and an interquartile range of 10. Class B has a median score of 78 and an interquartile range of 22. Which class has more spread in the middle half of its scores?

Accepted Answer

Class B has more spread in the middle half of its scores because it has the larger interquartile range.

Question 10

Find the five-number summary for this data set: 6, 8, 10, 11, 14, 16, 18, 20.

Accepted Answer

The five-number summary is minimum 6, first quartile 9, median 12.5, third quartile 17, and maximum 20.

Question 11

The temperatures for one week were 68, 70, 71, 72, 74, 75, and 83 degrees. Which display would better show the exact temperatures, a stem-and-leaf plot or a box plot?

Accepted Answer

A stem-and-leaf plot would better show the exact temperatures because it lists each individual data value while still organizing the data.

Question 12

A back-to-back stem-and-leaf plot compares two teams' points in games. Team Red values are 21, 24, 26, 28, 31, 33, and 35. Team Blue values are 18, 20, 22, 23, 25, 27, and 29. Which team has the higher median score?

Accepted Answer

Team Red has the higher median score. Team Red's median is 28, and Team Blue's median is 23.

Question 13

Use the 1.5 times IQR rule to check for outliers in this data set: 10, 12, 13, 15, 17, 18, 20, 45. The first quartile is 12.5 and the third quartile is 19. What value is an outlier?

Accepted Answer

The value 45 is an outlier. The IQR is 6.5, so 1.5 times the IQR is 9.75. The upper fence is 28.75, and 45 is greater than 28.75.

Question 14

A student made a box plot for the data 3, 5, 7, 8, 9, 11, 12. The student put the median line at 8 and the box from 5 to 11. Is the box correct? Explain.

Accepted Answer

The median line at 8 is correct, but the box is not correct. The lower half is 3, 5, 7, so Q1 is 5, and the upper half is 9, 11, 12, so Q3 is 11. The box from 5 to 11 is correct, so there is no error in the box.

Question 15

Two box plots show the number of minutes students exercised. Group X has a median of 35 minutes and an IQR of 12 minutes. Group Y has a median of 42 minutes and an IQR of 12 minutes. What can you conclude about the centers and spreads?

Accepted Answer

Group Y has the higher center because its median is 42 minutes compared with 35 minutes for Group X. The middle halves have the same spread because both groups have an IQR of 12 minutes.

Stem-and-Leaf Plots and Box Plots

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