EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Averages and Range
Averages and range · Interpreting and representing data · Lesson 5 of 6 · 15 marks · 25 minutes
Name Date
Answer all questions. Show your working. Questions 1 and 5 are non-calculator.
Question 1 NON-CALCULATOR [2 marks]
Here are six numbers: 7, 3, 9, 4, 7, 12. (a) Find the median. (b) Find the range.
Question 2 CALCULATOR [3 marks]
The table shows the number of goals scored by a football team in 20 matches. Goals 0: 4 matches. Goals 1: 7 matches. Goals 2: 5 matches. Goals 3: 3 matches. Goals 4: 1 match. Work out the mean number of goals per match.
Question 3 CALCULATOR [4 marks]
The weights, w kg, of 40 parcels are recorded. 0 < w ≤ 2: 6 parcels. 2 < w ≤ 4: 15 parcels. 4 < w ≤ 6: 12 parcels. 6 < w ≤ 8: 7 parcels. Work out an estimate for the mean weight of the parcels.
Question 4 CALCULATOR [1 mark]
For the parcels in the last question, write down the modal class.
Question 5 NON-CALCULATOR [2 marks]
The mean of five numbers is 8. Four of the numbers are 3, 7, 9 and 12. Find the fifth number.
Question 6 CALCULATOR [3 marks]
Class A has 20 students. Their mean test score is 64. Class B has 25 students. Their mean test score is 73. Work out the mean score of all 45 students.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
(a) In order: 3, 4, 7, 7, 9, 12. The median is (7 + 7)/2 = 7. (b) 12 − 3 = 9.
▸ (a) 7 B1
▸ (b) 9 B1
Question 2 [3 marks]
Total goals: 0 × 4 + 1 × 7 + 2 × 5 + 3 × 3 + 4 × 1 = 30. Mean = 30/20 = 1.5.
▸ At least three products of goals × frequency correct M1
▸ 30 ÷ 20 M1
▸ 1.5 A1
Question 3 [4 marks]
Midpoints 1, 3, 5, 7. 6 × 1 + 15 × 3 + 12 × 5 + 7 × 7 = 6 + 45 + 60 + 49 = 160. 160/40 = 4 kg.
▸ Midpoints used: 1, 3, 5, 7 M1
▸ At least three products of frequency × midpoint correct M1
▸ 160 ÷ 40 M1
▸ 4 (kg) A1
Question 4 [1 mark]
2 < w ≤ 4
▸ 2 < w ≤ 4 B1
Question 5 [2 marks]
Total = 5 × 8 = 40. 3 + 7 + 9 + 12 = 31. The fifth number is 40 − 31 = 9.
▸ 40 or 31 seen M1
▸ 9 A1
Question 6 [3 marks]
Class A total: 20 × 64 = 1280. Class B total: 25 × 73 = 1825. Mean = (1280 + 1825)/45 = 3105/45 = 69.
▸ 1280 or 1825 P1
▸ (1280 + 1825) ÷ 45 P1
▸ 69 A1