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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Estimating the mean from a grouped frequency table

Using class midpoints.

9 original questions, 35 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

The table shows the number of children in each of 20 families.

Number of childrenFrequency
03
18
26
33

Work out the mean number of children per family.

3 marks
Show answer
1.45
2

The grouped frequency table shows the time, t minutes, that 30 pupils took to get to school.

Time (t minutes)Frequency
0 < t ≤ 104
10 < t ≤ 209
20 < t ≤ 3012
30 < t ≤ 405
  1. Write down the modal class.
  2. Work out an estimate for the mean time.
4 marks
Show answer
a) 20 < t <= 30 b) 21
3

The table shows information about the time, t minutes, that 30 customers waited at a garage.

Time (t minutes)Frequency
0 < t ≤ 104
10 < t ≤ 209
20 < t ≤ 3012
30 < t ≤ 405

Work out an estimate for the mean waiting time.

3 marks
Show answer
21 minutes
4

The table shows information about the masses, m kg, of 40 parcels handled by a courier.

Mass (m kg)Frequency
0 < m ≤ 27
2 < m ≤ 410
4 < m ≤ 614
6 < m ≤ 89

Calculate an estimate for the mean mass of the parcels.

3 marks
Show answer
4.25 kg
5

The table shows information about the lengths, l cm, of 40 courgettes grown on an allotment.

Length (l cm)Frequency
10 < l ≤ 206
20 < l ≤ 3011
30 < l ≤ 4013
40 < l ≤ 5010
  1. Write down the class interval that contains the median.
  2. Work out an estimate for the mean length.
4 marks
Show answer
a) 30 < l <= 40 b) 31.75 cm
6

The table shows information about the times, t seconds, taken by 40 swimmers to complete one length of a pool.

Time (t seconds)Frequency
20 < t ≤ 308
30 < t ≤ 4015
40 < t ≤ 5012
50 < t ≤ 605
  1. Work out an estimate for the mean time.
  2. Explain why your answer to part (a) is an estimate.
4 marks
Show answer
a) 38.5 seconds b) Because the data is grouped, the exact times are unknown and midpoints are used
7

The table shows the heights, h cm, of 20 plants.

Height (h cm)Frequency
140 ≤ h < 1503
150 ≤ h < 1608
160 ≤ h < 1706
170 ≤ h < 1803
  1. Work out an estimate for the mean height.
  2. Explain why your answer to part (a) is only an estimate.
3 marks
Show answer
a) 159.5 b) We do not know the exact heights, only which class they are in, so we assume each is at the midpoint
8

The table shows information about the distances, d km, that 40 employees travel to work.

Distance (d km)Frequency
0 < d ≤ 59
5 < d ≤ 1016
10 < d ≤ 1511
15 < d ≤ 204
  1. Work out an estimate for the mean distance travelled.
  2. Write down the modal class.
  3. Work out the fraction of the employees who travel more than 10 km. Give your fraction in its simplest form.
5 marks
Show answer
a) 8.75 km b) 5 < d <= 10 c) 3/8
9

The table shows information about the heights, h cm, of 40 students.

Height (h cm)Frequency
140 < h ≤ 1506
150 < h ≤ 16014
160 < h ≤ 17016
170 < h ≤ 1804
  1. Work out an estimate for the mean height.
  2. Work out the percentage of the students who are more than 160 cm tall.
  3. Explain why your answer to part (a) is only an estimate.
6 marks
Show answer
a) 159.5 cm b) 50% c) The data is grouped so the exact heights are unknown; each class is represented by its midpoint

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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