Worksheet: Box-and-Whisker Plots

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

Q1:

This is a box-and-whisker plot for the test scores of a chemistry test. What is the median score?

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 7 5 %
  • B 1 2 . 5 %
  • C 9 0 %
  • D 5 0 %
  • E 2 5 %

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?

Q5:

The test scores for a physics test are displayed in the following box-and-whisker plot. Determine the percent of students who had scores between 85 and 120.

  • A 2 5 %
  • B 5 0 %
  • C 7 5 %
  • D 5 2 %

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:

Olivia 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.

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

  • A
  • B
  • C
  • D
  • E

Q8:

Look at the box-and-whisker plot. Give a reason why the line inside the box is further to the right.

  • AThe median is closer to Q3 than Q1.
  • BThe mode is 49.
  • CThe mean is about 49.
  • DThe person who made the graph messed up.

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 22C and 24C?

On roughly what percentage of days was the temperature greater than 24C?

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 3656?

  • 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?

  • A 5 0 %
  • B 1 0 0 %
  • C 2 5 %
  • D 6 8 %
  • E 7 5 %

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 50% 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.

Q17:

The given box-and-whisker plot represents the test scores for a trigonometry test. Determine the percent of the scores that are greater than or equal to 65.

  • A 5 2 %
  • B 7 5 %
  • C 2 5 %
  • D 5 0 %

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 𝑥, 𝑦, 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 𝑥 and 𝑦?

  • A 𝑥 = 3 9 7 , 𝑦 = 3 7 7
  • B 𝑥 = 3 8 7 , 𝑦 = 4 0 3
  • C 𝑥 = 3 7 7 , 𝑦 = 3 9 7
  • D 𝑥 = 3 8 7 , 𝑦 = 3 9 7
  • E 𝑥 = 3 9 7 , 𝑦 = 3 7 5

Q21:

The lower quartile, median, and upper quartile of a data set are 𝑥, 𝑦, 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 𝑥 and 𝑦?

  • A 𝑥 = 2 1 7 , 𝑦 = 2 0 2
  • B 𝑥 = 2 1 2 , 𝑦 = 2 2 2
  • C 𝑥 = 2 0 2 , 𝑦 = 2 2 2
  • D 𝑥 = 2 0 2 , 𝑦 = 2 1 7
  • E 𝑥 = 2 1 2 , 𝑦 = 2 1 7

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 50% 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

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