GCSE Exam Questions on Averages Grade E Questions
1. Work out the median of these 15 numbers.
3, 8, 8, 6, 4, 2, 8, 9, 4, 5, 1, 5, 7, 8, 9
……….
(Total 2 marks)
2. Five boxes are weighed. Their weights are given below.
3 kg, 11 kg, 5 kg, 20 kg, 11 kg, Write down the range of their weights.
…….………….. kg
(Total 1 mark)
3. Chloe made a list of her homework marks.
4 5 5 5 4 3 2 1 4 5 (a) Write down the mode of her homework marks.
……….
(1) (b) Work out her mean homework mark.
……….
(2) (Total 3 marks)
4. Here are the test marks of 6 girls and 4 boys. Girls: 5 3 10 2 7 3
Boys: 2 5 9 3
(a) Write down the mode of the 10 marks.
………
(b) Work out the median mark of the boys.
………
(2) (c) Work out the range of the girls’ marks.
………
(1) (d) Work out the mean mark of all 10 students.
………
(2) (Total 6 marks) Grade C Questions
5. 22 students took a short test.
The table gives information about their marks in the test.
Mark Frequency
7 1
8 6
9 5
10 10
(a) Write down the modal mark.
……….
(1) (b) Work out the range of the marks.
……….
(1) (c) Work out the mean mark.
………..
(3) (Total 5 marks)
6. Sarah watched a water ride at a theme park.
She counted the number of people in each of 20 boats. These numbers are shown below.
2 3 1 2 2 3 4 5 4 1 1 2 2 3 2 4 5 4 2 4 (a) Complete the frequency table.
Number of people in a boat Tally Frequency 1 2 3 4 5 (2) (b) Write down the mode of the number of people in a boat.
...
(1) Emily asked 5 people the number of rides each of them had been on.
The numbers are shown below.
6 8 7 6 10
(c) Work out the mean number of rides per person.
...
(3) (Total 6 marks)
7. 20 students scored goals for the school hockey team last month. The table gives information about the number of goals they scored.
Goals scored Number of students
1 9
2 3
3 5
4 3
(a) Write down the modal number of goals scored.
(b) Work out the range of the number of goals scored.
...
(1)
(c) Work out the mean number of goals scored.
...
(3) (Total 5 marks)
8. Rosie had 10 boxes of drawing pins.
She counted the number of drawing pins in each box. The table gives information about her results.
Number of
drawing pins Frequency
29 2
30 5
31 2
32 1
(a) Write down the modal number of drawing pins in a box.
...
(1) (b) Work out the range of the number of drawing pins in a box.
...
(1) (c) Work out the mean number of drawing pins in a box.
...
(3) (Total 5 marks)
9. The table shows the number of orders received each month by a small company.
Month Jan Feb Mar Apr May Jun Jul Aug
Number of
orders received 23 31 15 11 19 16 20 13
Work out the first two 4-month moving averages for this data.
... and ...
(Total 3 marks)
10. The grouped frequency table shows information about the weights, in kilograms, of 20 students, chosen at random from Year 11.
Weight (w kg) Frequency 50 ≤w < 60 7 60 ≤w < 70 8 70 ≤w < 80 3 80 ≤w < 90 2 There are 300 students in Year 11.
Work out an estimate for the number of students in Year 11 whose weight is between 50 kg and 60 kg.
………
11. Charles found out the length of reign of each of 41 kings. He used the information to complete the frequency table.
Length of reign
(L years) Number of kings 0 < L≤ 10 14
10 < L≤ 20 13 20 < L≤ 30 8 30 < L≤ 40 4 40 < L≤ 50 2
(a) Write down the class interval that contains the median.
….……….
(2) (b) Calculate an estimate for the mean length of reign.
………. years
(4) (Total 6 marks)
Answers
1. 6 2
1 2 3 4 4 5 5 6 7 8 8 8 8 9 9
M1 : 1 Mark for ordering
A1: 1 mark for correct answer only.
[2] 2. 17 1 20 – 3 B1 [1] 3. (a) 5 1 B1 (b) 3.8 2 4 + 5 + 5 + 5 + 4 + 3 + 2 + 1 + 4 + 5 = 38 mean = 38 ÷ 10 = 3.8
M1 : 1 Mark for attempt to add and ÷ 10 or 3.7 or 3.9 seen A1: 1 mark for correct answer 3.8
[3]
4. (a) 3 1
B1
(b) 4 2
2 3 5 9
M1 : 1 mark for ordering A1: 1 mark for correct anwer
(c) 8 1
B1
(d) 4.9 2
49 ÷ 10
M1 : 1 Mark for add and divide by 10 A1 : 1 mark for correct answer 4.9 oe
[6]
5. (a) 10 1
B1 for 10
(c) 10 3 1×7+6×8+5×9+10×10 (200)
[1×7+6×8+5×9+10×10] ÷ 20
M1: 1 mark for sum of freq × mark M1(dep.) for “200” ÷ 20
A1 for 10
[5]
6. (a) 3, 7, 3, 5, 2 2
Complete tally and frequency
B2 for all 5 frequencies correct (B1 for any 3 correct)
SC B1 B0 for tallies only, all tallies correct
(b) 2 1 B1 f.t. (dep on B1) (c) 7.4 3 6 + 8 + 7 + 6 + 10 “37” ÷ 5 M1 for 6 + 8 + 7 + 6 + 10 or 37 seen M1 dep for “37” ÷ 5 A1 cao [6] 7. (a) 1 1 B1 for 1 (b) 3 1 B1 for 3 (c) 2.1 3 9 × 1 + 3 × 2 + 5 × 3 + 3 × 4 (= 42) “42” ÷ 20
M1 for 9 × 1, 3 × 2, 5 × 3, 3 × 4 or for 42 seen M1 (dep) for “42” ÷ 20 A1 for 2.1 or 2 10 1 or 2 20 2 [5] 8. (a) 30 1 B1 cao (b) 3 1 B1 cao
(c) 30.2 3 2 × 29 = 58 5 × 30 = 150 2 × 31 = 62 1 × 32 = 32 2 . 30 10 302 =
M1 for freq × no pins
M1 (dep on 1st M1) for totalling and ÷ 10 A1 for 30.2 cao [5] 9. 20 4 11 15 31 23+ + + 19 4 19 11 15 31+ + + 3
M1 for finding the mean of any 4 consecutive months A1 for 20 A1 for 19 [3] 10. 105 3 300 20 7 × M1foreither 20 7 oeor 20 300 oe(condoneslipin∑f) M1for 300 20 7 × oe(condoneslipin∑f)or 300 105 seen A1cao [3] 11. (a) 10< L ≤ 20 2
M1foruseofcumulativefrequencytofindthe20.5thor21st value
(b) 16.95 4 (5 × 14) + (15 × 13) + (25 × 8) + (35 × 4) +
(45 × 2) = 70 + 195 + 200 + 140 + 90 = 695 695 ÷ 41 =
M1∑fxusingvalueswithinintervals(includingends), atleast4consistently
M1(dep)∑fxusingmidpoints M1(depon1stM1)"695"÷41
