# Worksheet: Box-and-Whisker Plots

In this worksheet, we will practice constructing and analyzing data from box-and-whisker plots.

**Q2: **

Which set of data could be represented by the given box-and-whisker plot?

- A79, 76, 76, 78, 72, 79, 80, 72
- B76, 72, 76, 78, 71, 80, 73, 76
- C80, 80, 78, 72, 76, 71, 76, 76
- D72, 72, 78, 80, 78, 76, 76, 76
- E78, 72, 78, 76, 76, 72, 76, 81

**Q3: **

State if the following is true or false: There are more data values in the interval 36–80 than there are in the interval 64–80.

- Atrue
- Bfalse

**Q4: **

The times, rounded to the nearest second, of a group of students running a 400-meter race are represented on the box plot shown.

What was the median time taken?

What was the lower quartile?

What was the longest time taken?

What percentage of students are represented by the times within the box?

- A
- B
- C
- D
- E

Is the median time closer to the lower or upper quartile?

- Aupper quartile
- Blower quartile

What was the overall range of times taken?

What was the interquartile range of times taken?

**Q6: **

Simon has calculated the following information from a data set about the ages of people present on a Saturday morning in a swimming pool:

lowest value: 7

lower quartile: 10

median: 15

upper quartile: 22

highest value: 31

Simon draws a box plot from the data. Which of the following box plots did Simon draw?

- A
- B
- C
- D
- E

**Q7: **

Chloe counted the number of cars that were parked on her road at 8:00 pm on 11 successive days. She presented her data as a list: 3, 8, 12, 6, 5, 6, 7, 9, 4, 10, 8.

She was surprised to find that the minimum number of cars that she counted was 3 and that the maximum number of cars was 12.

Calculate the median number of cars.

Calculate the lower quartile for the number of cars.

Calculate the upper quartile for the number of cars.

Chloe draws a box plot of the data. Which of the following is correct?

- A
- B
- C
- D
- E

**Q9: **

The box plot shows the daily temperatures at a seaside resort during the month of August.

On roughly what percentage of days was the temperature between and ?

On roughly what percentage of days was the temperature greater than ?

What was the median temperature?

What was the maximum temperature recorded?

What was the minimum temperature recorded?

What was the lower quartile of the temperatures?

What was the upper quartile of the temperatures?

What was the interquartile range of the temperatures?

What was the range of the temperatures?

**Q10: **

Is half of the data in the interval ?

- AYes
- BNo

**Q11: **

How many summary statistics are represented on a box plot?

**Q12: **

What percentage of data values are contained within the box part of a box-and-whisker plot?

**Q13: **

What do the whiskers on a box plot show?

- Athe full range of included data
- Bthe variability of the data in the upper quartile only
- Cthe interquartile range
- Dthe variability of the data in the lower quartile only
- Ethe middle of the data

**Q14: **

Which type of average is represented on a box plot?

- Amode
- Bmean
- Cmedian
- Drange

**Q15: **

Is half the data above 48?

- Ayes
- Bno

**Q16: **

Using the given box-and-whisker plot, find the range of the data.

**Q18: **

State whether the following statement is true or false: The data in the interval between the lower quartile and the median is more spread out than the data in the interval between the median and the upper quartile.

- Afalse
- Btrue

**Q19: **

Which of the following sets of data can be represented by this box-and-whisker plot?

- A17, 20, 18, 19, 20, 16, 16
- B16, 14, 27, 20, 22, 17, 16
- C19, 19, 17, 14, 22, 20, 21
- D17, 16, 18, 14, 20, 19, 22
- E18, 19, 14, 19, 16, 22, 17

**Q20: **

The lower quartile, median, and upper quartile of a data set are , , and 417, respectively. In a box-and-whisker plot representing the data, the median separates the box into two equal parts. Which of the following are possible values of and ?

- A,
- B,
- C,
- D,
- E,

**Q21: **

The lower quartile, median, and upper quartile of a data set are , , and 247, respectively. In a box-and-whisker plot representing the data, the box between the median and the upper quartile is twice as long as the box between the median and the lower quartile. Which of the following are possible values of and ?

- A,
- B,
- C,
- D,
- E,

**Q22: **

Which of the following sets of data has an interquartile range of 7 and two outliers?

- A25, 24, 22, 54, 9, 33, 25, 22
- B28, 29, 34, 23, 34, 20, 35, 39
- C30, 35, 34, 23, 22, 35, 40, 83
- D9, 25, 22, 24, 25, 24, 33, 54
- E1, 8, 11, 10, 7, 10, 10, 45

**Q23: **

A set of data’s minimum is 3.44, its lower quartile is 7.42, its median is 7.74, its upper quartile is 14.02, and its maximum is 17.74. Between which two values does the middle of the data lie?

- A7.74 and 17.74
- B7.74 and 14.02
- C3.44 and 7.74
- D7.42 and 7.74
- E7.42 and 14.02

**Q24: **

The table shows a five-number summary of the ages of the members of a squash club.

Minimum | Lower Quartile | Median | Upper Quartile | Maximum |
---|---|---|---|---|

19 | 28 | 32 | 45 | 68 |

Approximately, what proportion of the club’s members are younger than 32 years old?

Approximately, what percentage of the club’s members are between 32 and 45 years old?

Approximately, what percentage of the club’s members are between 28 and 68 years old?

**Q25: **

James was calculating the measures of variation for the following set of data: 79, 88, 96, 108, 110, 117, 118, 134, 136. His answers are recorded in the table. Which of his answers is wrong? What is the correct measure?

Measure of Variation | Median | Lower Quartile | Upper Quartile | Interquartile Range | Range |
---|---|---|---|---|---|

James’s Answer | 110 | 92 | 126 | 34 | 55 |

- Aupper quartile, 118
- Binterquartile range, 109
- Cmedian, 117
- Drange, 57
- Elower quartile, 93