# Exam-Style Question on Box Plots

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 496. This question is similar to one that appeared on a GCSE Higher paper in 2019. The use of a calculator is not allowed.

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?

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