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
The stem-and-leaf diagram shows how many minutes late each of $19$ trains was when it arrived at a station on Monday.

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

Key: $1 \mid 3$ represents $13$ minutes
(a) Find the median.

(1 mark)
(b) Work out the range.

(2 marks)

On Tuesday, the median was $9$ minutes and the range was $31$ minutes.
(c) Compare how late the trains were on Monday with how late they were on Tuesday.

(2 marks)
Level 3 · 5 marksTry it
2
A helpline records how long, in seconds, each of $24$ callers waited before their call was answered.

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

Key: $1 \mid 2$ represents $12$ seconds

Priya says,

"More than three quarters of these callers waited less than $30$ seconds."

Is Priya correct?

You must show how you get your answer.

(3 marks)
Level 3 · 3 marksTry it
3
The back-to-back stem-and-leaf diagram shows the scores, out of $50$ , of some Year 10 students and some Year 11 students in a spelling test.

$\begin{array}{r|c|l} \llap{\text{Year 10}} & & \rlap{\text{Year 11}} \\[2pt] 8 & 1 & \\ 9~~~7~~~5~~~2 & 2 & 4~~~8 \\ 8~~~6~~~3~~~1 & 3 & 3~~~5~~~6~~~9 \\ 4~~~0 & 4 & 1~~~5~~~7 \end{array}$

Key: $1 \mid 3 \mid 5$ represents $31$ for Year 10 and $35$ for Year 11
(a) Work out the median score for Year 10.

(1 mark)
(b) Work out the median score for Year 11.

(1 mark)
(c) Compare the average and consistency of the scores of the two year groups.

You must show your working.

Average ..............................

Consistency ..............................

(3 marks)
Level 3 · 5 marksTry it
4
Here is a question and an incorrect solution.

Question

The stem-and-leaf diagram shows the number of text messages each of $17$ students sent one day.

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

Key: $1 \mid 2$ represents $12$ messages

Find the median.

Solution

The middle row has stem $2$ . The middle leaf on that row is $6$ . So the median is $26$ messages.

Describe the error made and write out a correct solution.

(3 marks)
Level 3 · 3 marksTry it
5
The stem-and-leaf diagram shows the temperature, in °C, at midday in a town on $16$ days.

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

Key: $2 \mid 1$ represents $21$ °C
(a) One of these days is chosen at random.

Work out the probability that the temperature at midday was more than $25$ °C.

(2 marks)

On the next day, the temperature at midday was $26$ °C.
(b) Work out the median temperature for all $17$ days.

(2 marks)
Level 3 · 4 marksTry it

2 more questions on stem-and-leaf diagrams (including back-to-back)

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