**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 *