Robinson Tuition
Grade 4 · Foundation and Higher · free GCSE maths worksheet

Comparing distributions

Using an average and the range.

8 original questions, 29 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Here are the test results for two classes.

MeanRange
Class 9A6240
Class 9B5818

Write down two comparisons between the results of the two classes.

2 marks
Show answer
The mean of 9A (62) is higher, so on average 9A did better; the range of 9B (18) is smaller, so 9B results were more consistent
2

The stem and leaf diagram shows the number of press-ups 11 students did in one minute.

StemLeaves
06  8
11  3  5  7  9
22  4  6  8

Key: 1 | 1 = 11 press-ups

  1. Find the median number of press-ups.
  2. Find the range of the number of press-ups.
3 marks
Show answer
a) 17 b) 22
3

Two hockey teams played five matches each. This table shows the number of goals each team scored.

Match 1Match 2Match 3Match 4Match 5
Team A20413
Team B12232
  1. Work out the mean and the range for each team.
  2. Which team is more consistent? Give a reason.
4 marks
Show answer
a) Team A mean 2, range 4; Team B mean 2, range 2 b) Team B, because its range is smaller
4

Nine boys and nine girls sat the same quiz. Their scores are shown in two stem and leaf diagrams.

Boys

StemLeaves
05
12  8
23  7
31  5  8
44

Girls

StemLeaves
21  4  6  8
30  3  5  7
40

Key: 2 | 1 = 21 points

Compare the boys' scores with the girls' scores.

3 marks
Show answer
Girls' median (30) is higher than boys' median (27), so the girls scored more on average; girls' range (19) is smaller than boys' range (39), so the girls' scores were more consistent
5

A town council records how many minutes late the 12 bus and the 15 bus were on five days.

MonTueWedThuFri
Route 1247293
Route 1565757
  1. Work out the mean delay and the range for each route.
  2. Sunita says, "Route 12 is better because its mean delay is smaller." Give one reason why Route 15 might still be seen as the more reliable route.
4 marks
Show answer
a) Route 12 mean 5 range 7; Route 15 mean 6 range 2 b) Route 15 has a smaller range, so its delays are more consistent and predictable
6

The stem and leaf diagram shows the times, in minutes, that 15 students in Class A took to finish a puzzle.

StemLeaves
21  4  8
30  2  3  5  7  9
42  4  6  8
50  3

Key: 2 | 1 = 21 minutes

For Class B, the median time was 38 minutes and the range of the times was 15 minutes.

  1. Find the median time for Class A.
  2. Find the range of the times for Class A.
  3. Compare the times of Class A with the times of Class B.
4 marks
Show answer
a) 37 minutes b) 32 minutes c) Class A slightly faster on average (lower median); Class B more consistent (smaller range)
7

A gardener grew 12 bean plants using Fertiliser A and 12 bean plants using Fertiliser B. The stem and leaf diagrams show the heights of the plants, in centimetres, after six weeks.

Fertiliser A

StemLeaves
14  7
21  3  6  8
30  2  5  7
41  3

Fertiliser B

StemLeaves
25  7  9
31  2  4  6  8  9
40  2  5

Key: 2 | 5 = 25 cm

The gardener wants to use the fertiliser that grows taller, more consistent plants. Compare the two distributions and state which fertiliser the gardener should choose.

5 marks
Show answer
Fertiliser B: its median (35 cm) is higher than A's (29 cm), so B plants are taller on average, and its range (20 cm) is smaller than A's (29 cm), so B plants are more consistent
8

Nine students in Year 7 and nine students in Year 11 ran a race. Here are their times, in seconds.

Year 7:  12  15  15  18  20  21  24  26  28

Year 11:  8  10  13  14  16  19  22  25  27

Compare the times of the Year 7 students with the times of the Year 11 students.

4 marks
Show answer
Year 11 median (16 s) is lower than Year 7 median (20 s), so Year 11 were faster on average; Year 7 range (16 s) is smaller than Year 11 range (19 s), so Year 7 times were more consistent

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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