GCSE · Data representation

Stem-and-leaf diagrams (including back-to-back)Exam-style questions

A stem-and-leaf diagram keeps every value and shows the shape of the data at once. How to draw an ordered diagram with a key, how to read the mode, median and range (and the quartiles) by counting leaves, and how to compare two groups on a back-to-back diagram with an average and a spread, in context.

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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

1
A doctor measures the resting pulse rates, in beats per minute, of $15$ adults who swim regularly and $17$ adults who do not.

The back-to-back stem-and-leaf diagram shows the results.

$\begin{array}{r|c|l} \llap{\text{Swimmers}} & & \rlap{\text{Non-swimmers}} \\[2pt] 8~~~7~~~5~~~2 & 5 & \\ 8~~~6~~~4~~~3~~~1~~~0 & 6 & 1~~~4~~~7~~~9 \\ 7~~~5~~~3~~~1~~~0 & 7 & 0~~~2~~~2~~~5~~~6~~~8 \\ & 8 & 0~~~3~~~4~~~7~~~9 \\ & 9 & 2~~~6 \end{array}$

Key: $4 \mid 6 \mid 7$ represents $64$ for a swimmer and $67$ for a non-swimmer

Make two comparisons between the pulse rates of the two groups.

Include values to support your comparisons.

(4 marks)
Level 4 · 4 marksTry it
2
Here are the distances, in metres, that the $11$ students in Group A and the $11$ students in Group B threw a cricket ball.

Group A: $24$ , $31$ , $18$ , $27$ , $35$ , $22$ , $29$ , $41$ , $33$ , $26$ , $30$

Group B: $36$ , $33$ , $45$ , $39$ , $31$ , $46$ , $42$ , $35$ , $38$ , $44$ , $40$
(a) Draw a back-to-back stem-and-leaf diagram to show this information.

(3 marks)
(b) Compare the distances thrown by the two groups.

(3 marks)
Level 4 · 6 marksTry it
3
A museum records how long, in minutes, visitors spend in its dinosaur gallery.

The stem-and-leaf diagram shows the times for $19$ visitors on Saturday.

$\begin{array}{r|lllll} 2 & 5 & 8 \\ 3 & 0 & 4 & 6 & 9 \\ 4 & 1 & 2 & 2 & 5 & 7 \\ 5 & 0 & 3 & 6 & 8 \\ 6 & 4 & 7 \\ 7 & 1 & 6 \end{array}$

Key: $4 \mid 1$ represents $41$ minutes
(a) Find the median time for Saturday.

(1 mark)
(b) Work out the interquartile range of the times for Saturday.

(2 marks)

The box plot shows information about the times for the visitors on Sunday.(c) Compare the distribution of the times on Saturday with the distribution of the times on Sunday.

(2 marks)
Level 4 · 5 marksTry it
4
The stem-and-leaf diagram shows the masses of $12$ dogs at a rescue centre.

Two of the leaves are missing.

$\begin{array}{r|llll} 1 & 8 \\ 2 & 3 & 5 & 9 \\ 3 & 1 & 4 & \square & 8 \\ 4 & 0 & 2 & 6 \\ 5 & \square \end{array}$

Key: $3 \mid 1$ represents $31$ kg

The median mass is $35.5$ kg.

The range of the masses is $35$ kg.

Work out the masses of the two dogs whose leaves are missing.

(4 marks)
Level 4 · 4 marksTry it