# Exam-Style Questions on Box Plots

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

### 1.

GCSE Higher

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.

• Shortest time 30 minutes
• Longest time 5 hours
• Lower quartile 90 minutes
• Interquartile range 2 hours
• Median time 2 hours 30 minutes

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.

(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.

(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.

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

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

 Median Lower quartile Upper quartile Shortest Tallest

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

 Median 160 Lower quartile 143 Upper quartile 172 Shortest 110 Tallest 199

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

(b) Is Poppy correct?

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?

### 7.

IB Analysis and Approaches

A number of organically-grown carrots were measured (in centimetres) and the results recorded. The following box and whisker diagram shows a summary of the results where L and U are the lower and upper quartiles respectively. The diagram is not drawn to scale.

The interquartile range is 8cm and there are no outliers in the results.

Find the maximum possible value of L.

Hence, find the maximum possible value of U.

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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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