GCSE · Cumulative frequency & box plots

Box plotsExam-style questions

What each of the five marks on a box plot means, why the box holds the middle 50% of the data, and why a longer section means the data there is more spread out — never that there is more of it.

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12 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The box plot gives information about the masses, in kilograms, of the dogs at a rescue centre.(a) Write down the median mass.

(b) Work out the range of the masses.

(c) Work out the interquartile range of the masses.
Level 2 · 5 marksTry it
2
For the times taken by $60$ students to complete a puzzle: the shortest time was $5$ minutes, the lower quartile was $12$ minutes, the median was $20$ minutes, the upper quartile was $26$ minutes and the longest time was $41$ minutes.

(a) Work out the interquartile range. [1]

(b) How many of the students took $26$ minutes or longer? [1]

A second class had a median of $24$ minutes and an interquartile range of $10$ minutes.

(c) Compare the times of the two classes. [1]
Level 2 · 3 marksTry it
3
The box plot shows information about the times, in minutes, that students in class A took to finish a test.(a) Write down the interquartile range for class A. (1 mark)

For class B: the shortest time was $12$ minutes, the lower quartile was $20$ minutes, the median was $26$ minutes, the upper quartile was $33$ minutes and the longest time was $40$ minutes.
(b) Compare the distribution of the times for class A with the distribution of the times for class B. (2 marks)
(c) What fraction of the students in class A took longer than $30$ minutes? (1 mark)
Level 3 · 4 marksTry it
4
A gardener measures the heights of $40$ sunflowers.

The shortest sunflower is $84$ cm tall and the tallest is $186$ cm tall.

The median height is $120$ cm, the lower quartile is $108$ cm and the upper quartile is $156$ cm.

(a) Draw a box plot for this information.

(b) Work out the interquartile range of the heights.

(c) Work out how many of the sunflowers are taller than $156$ cm.
Level 3 · 5 marksTry it
5
The box plot gives information about the times, in minutes, taken by $200$ people to travel to work.(a) Work out the interquartile range of the times.

(b) Priya looks at the box plot and says, "Most of these people took between $35$ and $60$ minutes to travel to work, because that part of the box plot is much longer than any other part."

Is Priya correct? Give a reason for your answer.
Level 3 · 4 marksTry it

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