GCSE · Averages & range

Averages from a frequency tableExam-style questions

Mean, median, mode and range from a discrete frequency table — why the mean is the sum of the fx column divided by the total FREQUENCY, not by the number of rows, and how to run it backwards to find a missing frequency.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
The table shows the number of pets owned by $20$ students.
Pets $0$ $1$ $2$ $3$
Frequency $6$ $9$ $4$ $1$
Write down the modal number of pets.
Level 1 · 1 markTry it
2
A hockey team played 20 matches. The table shows the number of goals the team scored in each match.
Number of goals, $x$ Frequency, $f$
0 3
1 7
2 6
3 3
4 1
(a) Write down the modal number of goals.

(b) Work out the range of the number of goals.

(c) Work out the total number of goals the team scored in the 20 matches.
Level 2 · 4 marksTry it
3
The table shows the number of pets owned by $20$ students.
Pets $0$ $1$ $2$ $3$
Frequency $6$ $9$ $4$ $1$
Work out the total number of pets owned.
Level 2 · 2 marksTry it
4
The table shows the number of pets owned by each of $20$ students.
Number of pets 0 1 2 3
Frequency 5 8 4 3
(a) Work out the mean number of pets. (3 marks)

(b) Write down the median number of pets. (1 mark)
Level 3 · 4 marksTry it
5
The table shows the number of people travelling in each of 40 cars that passed a checkpoint.
Number of people, $x$ Frequency, $f$
1 14
2 12
3 8
4 4
5 2
Work out the mean number of people per car.
Level 3 · 3 marksTry it

Pets	$0$	$1$	$2$	$3$
Frequency	$6$	$9$	$4$	$1$

Number of goals, $x$	Frequency, $f$
0	3
1	7
2	6
3	3
4	1

Pets	$0$	$1$	$2$	$3$
Frequency	$6$	$9$	$4$	$1$

Number of pets	0	1	2	3
Frequency	5	8	4	3

Number of people, $x$	Frequency, $f$
1	14
2	12
3	8
4	4
5	2

6 more questions on averages from a frequency table

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