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Exam-Style Questions on Box Plots

Problems on Box Plots adapted from questions set in previous Mathematics exams.

1.

GCSE Higher
Box Plot

The box plot shows information about the distribution of the times (in minutes) groups of customers spend in a open-air restaurant.

(a) Calculate the interquartile range for the amount of time groups spend in this open-air restaurant.

The table below shows information about the distribution of the times (in minutes) groups of customers spend in an indoor restaurant.

  Minimum Lower Quartile Median Upper quartile Maximum
Time in minutes 30 45 62 82 94

(b) On the lower half of the grid above, draw a box plot for the information in the table.

(c) Hunter thinks that the total amount of time spend by all of the customers visiting the indoor restaurant is greater than the total amount of time spend by all of the customers visiting the open-air restaurant. Is Hunter correct? Explain your decision.


2.

GCSE Higher

Here is some information about the length of time children spent in a swimming pool at a holiday resort during a heat wave.

Draw a box plot to show this information.


3.

GCSE Higher

One day a theme park monitored the time spent by guests at six different areas of the park. The times are recorded in the box plots below.

Box and whisker plot

(a) Work out the range in times at Future Zone.

(b) At which area were visitor times the most consistent? Give a reason for your answer.

(c) Give one similarity and one difference between the distributions of the guest visiting times for Nature Park and Fantasy Land.

(d) Is it possible to work out from the box plots which area had the most visitors? Explain your answer.


4.

IB Studies

The distribution of daily average wind speed on an island over a period of 120 days is displayed on this box-and-whisker diagram.

(a) Write down the median wind speed.

(b) Write down the minimum wind speed.

(c) Find the interquartile range.

(d) Write down the number of days the wind speed was between 20 kmh-1 and 51 kmh-1.

(e) Write down the number of days the wind speed was between 9 kmh-1 and 68 kmh-1.


5.

IB Applications and Interpretation

Derek has put together a fantasy football squad and has recorded the heights of all the players in the squad rounded to the nearest centimetre. The data is illustrated in the following box and whisker diagram.

box and whisker diagram

(a) Write down the median height of the players.

(b) Write down the upper quartile height.

(c) Find the interquartile range of the heights.

The height of these players are normally distributed.

(d) Find the height of the tallest possible player that is not an outlier. Give your answer to the nearest centimetre.


6.

GCSE Higher

Poppy Pringle recorded the heights in centimetres of the sunflowers growing in her brother's and sister's gardens.

Sunflower

Here are the heights of the 19 sunflowers in her brother's garden:

$$94, 103, 110, 111, 123, 143, 150, 150, 151, 156, 157, 160, 170, 182, 201, 220, 250, 255, 231$$

(a) Complete the table below to show information about this data.

Median        
Lower quartile 
Upper quartile 
Shortest 
Tallest 

Here is some information about the sunflowers in Poppy's sister's garden:

Median160
Lower quartile143
Upper quartile172
Shortest110
Tallest199

Poppy says that the sunflowers in her brother's garden are shorter that those in her sister's garden.

(b) Is Poppy correct?

You must give a reason for your answer.

Poppy says that the sunflowers in her brother's garden vary more in height than those in her sister's garden.

(c) Is Poppy correct?

You must give a reason for your answer.


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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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