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 plots give information about the distances, in km, travelled to work by the employees at two companies.

Company A, which has $200$ employees:Company B, which has $120$ employees:(a) Work out how many of the employees at Company A travel more than $30$ km to work.

(b) Jordan says, "The box for Company B is much wider than the box for Company A, so more employees at Company B travel a distance between their own company's lower quartile and upper quartile."

Is Jordan correct? You must show your working.
Level 5 · 5 marksTry it
2
Sam is drawing a box plot for a set of data. He knows that
- the smallest value is $9$ ,
- the range is $46$ ,
- the median is $34$ ,
- the interquartile range is $18$ ,
- the median is $7$ more than the lower quartile.
(a) Work out the largest value.

(b) Work out the lower quartile.

(c) Work out the upper quartile.

(d) Sam says that the same number of values lie between the lower quartile and the median as lie between the upper quartile and the largest value.

Is Sam correct? Give a reason for your answer.
Level 5 · 6 marksTry it