Browse Averages & range

41 questions at your level

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

Mean, median, mode & range

15 questions

LessonNot started

\quad 3, \; 7, \; 4, \; 7, \; 9

. Write down the mode.

●●●●●Level 11 markStart

Here are five numbers:

\quad 3, \; 7, \; 4, \; 7, \; 9

. Work out the median.

●●●●●Level 12 marksStart

Here are five numbers:

\quad 3, \; 7, \; 4, \; 7, \; 9

. Work out the mean and the range.

●●●●●Level 13 marksStart

Here are the numbers of minutes a school bus was late on each of nine mornings.

0 \quad 4 \quad 2 \quad 1 \quad 6 \quad 2 \quad 1 \quad 1 \quad 1

(a) Write down the mode.

(b) Work out the median.

(c) Work out the range.

(d) Work out the mean.

●●●●●Level 26 marksStart

Here are five numbers.

4 \qquad 7 \qquad 9 \qquad 12 \qquad x

The mean of the five numbers is

9

(a) Work out the value of

x

. (2 marks)

(b) Work out the range of the five numbers. (1 mark)

●●●●●Level 23 marksStart

The mean of five numbers is

8

One of the numbers is removed. The mean of the remaining four numbers is

7.5

Work out the number that was removed. (3 marks)

●●●●●Level 23 marksStart

Eleven students each did as many press-ups as they could. Here are their results.

22 \quad 15 \quad 30 \quad 18 \quad 15 \quad 27 \quad 12 \quad 15 \quad 24 \quad 20 \quad 19

(a) Ravi says, "The median is

27

, because

27

is the middle number of the list."

Explain what is wrong with Ravi's method.

(b) Work out the median number of press-ups.

(c) Work out the mean number of press-ups. Give your answer correct to 1 decimal place.

●●●●●Level 35 marksStart

In their last seven matches, the numbers of goals scored by two teams were:

Ashby Town:

1, \; 2, \; 2, \; 3, \; 2, \; 4, \; 0

Byrne United:

0, \; 5, \; 1, \; 6, \; 0, \; 2, \; 0

(a) Show that the two teams have the same mean number of goals per match.

(b) Work out the range for each team.

(c) Use your answers to compare the goal scoring of the two teams.

●●●●●Level 36 marksStart

Here are two lists of numbers.

List A

\qquad 18 \qquad 35 \qquad 27 \qquad 40 \qquad 25

List B

\qquad 52 \qquad x \qquad 61 \qquad 38

mean of list A : mean of list B

= 2 : 3

Work out the value of

x

.

(5 marks)

●●●●●Level 35 marksStart

Seven pupils each solved a puzzle. Their times, in seconds, were:

32 \quad 41 \quad 38 \quad 35 \quad 44 \quad 39 \quad 36

(a) Work out the median of these seven times.

(b) Write down the range of these seven times.

An eighth pupil then solves the puzzle in

115

seconds.

(c) Work out the median of all eight times.

(d) Write down the range of all eight times.

(e) The mean of all eight times is

47.5

seconds. Explain why the median is a better description of a typical time for these eight pupils than the mean is.

●●●●●Level 47 marksStart

A small company has nine employees. Their annual salaries are:

£19 000, £21 000, £22 000, £21 000, £24 000, £23 000, £21 000, £26 000, £120 000

(a) Work out the mean salary.

(b) Work out the median salary.

(c) The owner wants to quote a single figure as "a typical salary at this company". State which of the mean and the median is the fairer figure to quote, and give a reason for your answer.

(d) The company also records the department each of the nine employees works in:

Sales, Sales, Admin, Sales, Workshop, Admin, Sales, Workshop, Admin

Write down the modal department, and explain why neither the mean nor the median can be used for this data.

●●●●●Level 48 marksStart

Here are five numbers.

12 \quad 7 \quad 15 \quad 9 \quad x

The mean of the five numbers is

13

.

(a) Work out the value of

x

.

(b) Work out the median of the five numbers.

●●●●●Level 45 marksStart

The table gives some information about the lengths, in minutes, of

60

films shown at a film festival.

	Length (minutes)
Shortest length	$84$
Longest length	$152$
Lower quartile	$97$
Upper quartile	$121$
Median	$108$

(a) Draw a box plot to represent this information.(3 marks)
(b) Work out an estimate for the number of these films with a length between

97

minutes and

121

minutes.

(1 mark)

Oscar says,

"The median is

108

minutes, so one of the films must be exactly

108

minutes long."
(c) Is Oscar correct? Give a reason for your answer.

(1 mark)

●●●●●Level 45 marksStart

(a) The mean of eight numbers is

21

.

One of the eight numbers is removed. The mean of the remaining seven numbers is

22

.

Work out the number that was removed.

(b) The mean of five numbers is

12

.

A sixth number is then included, and the mean of all six numbers is

13

.

Work out the sixth number.

●●●●●Level 56 marksStart

Thirty students took a test. The mean mark for all thirty students was

62

.

The twelve girls in the group had a mean mark of

65

.

(a) Work out the mean mark of the eighteen boys.

(b) Two more students then take the same test. The mean mark of all thirty-two students is

62.5

.

Work out the mean mark of the two extra students.

●●●●●Level 57 marksStart

Averages from a frequency table

12 questions

LessonNot started

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 11 markStart

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 24 marksStart

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 22 marksStart

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 33 marksStart

The table shows the number of books read last month by each of 31 students.

Number of books, $x$	Frequency, $f$
0	4
1	11
2	8
3	5
4	3

(a) Write down the modal number of books.

(b) Work out the median number of books.

●●●●●Level 33 marksStart

The table shows the number of times each of 50 pupils was late during one term.

Number of times late, $x$	Frequency, $f$
0	21
1	14
2	9
3	4
4	2

Ali says: "The mean is

2

, because

(0 + 1 + 2 + 3 + 4) \div 5 = 2

."

(a) Explain what is wrong with Ali's method.

(b) Work out the correct mean number of times a pupil was late.

●●●●●Level 34 marksStart

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 34 marksStart

The table shows information about the time,

t

minutes, that each of

20

students spent on homework one evening.

Time, $t$ (minutes)	Frequency
$0 < t \le 10$	4
$10 < t \le 20$	6
$20 < t \le 30$	8
$30 < t \le 40$	2

(a) Work out an estimate for the mean time spent on homework. (3 marks)
(b) Write down the modal class. (1 mark)

●●●●●Level 34 marksStart

The table gives information about the number of days each of 60 students was absent last term.

Number of days absent, $x$	Frequency, $f$
0	18
1	15
2	12
3	9
4	4
5	2

(a) Write down the range of the number of days absent.

(b) Work out the median number of days absent.

(c) Work out the mean number of days absent. Give your answer correct to 2 decimal places.

●●●●●Level 46 marksStart

A shop recorded the number of items bought by each of 80 customers. One frequency has been left out of the table.

Number of items, $x$	Frequency, $f$
1	26
2	21
3
4	9
5	6

(a) Work out the missing frequency.

(b) Work out the mean number of items bought per customer.

●●●●●Level 45 marksStart

The table shows the number of pets owned by each of the 24 pupils in a class.

Number of pets, $x$	Frequency, $f$
0	9
1	7
2	5
3	2
4	1

(a) Work out the mean number of pets owned by these 24 pupils.

(b) Six more pupils join the class. Each of these six pupils owns 3 pets.

Work out the mean number of pets owned by all 30 pupils.

●●●●●Level 46 marksStart

The table gives information about the number of people living in each house on one side of a street.

Number of people, $x$	Frequency, $f$
1	2
2	$y$
3	6
4	2

The mean number of people per house is

2.4

.

(a) Work out the value of

y

.

(b) Work out the median number of people per house.

●●●●●Level 56 marksStart

Estimating averages from grouped data

15 questions

LessonNot started

The table shows the times,

t

minutes, that

30

students took to finish a puzzle.

Time ( $t$ minutes)	Frequency
$0 < t \le 10$	$5$
$10 < t \le 20$	$18$
$20 < t \le 30$	$7$

Write down the modal class.

●●●●●Level 11 markStart

The table shows the times,

t

minutes, that

30

students took to finish a puzzle.

Time ( $t$ minutes)	Frequency
$0 < t \le 10$	$5$
$10 < t \le 20$	$18$
$20 < t \le 30$	$7$

Write down the midpoint of the class

10 < t \le 20

, and explain why an estimate of the mean uses midpoints.

●●●●●Level 12 marksStart

The table shows information about the time,

t

minutes, that each of 40 customers waited to be served in a post office.

Time, $t$ (minutes)	Frequency
$0 < t \le 2$	15
$2 < t \le 4$	9
$4 < t \le 6$	10
$6 < t \le 8$	6

(a) Write down the modal class.

(b) Find the class interval that contains the median.

●●●●●Level 23 marksStart

The table shows the ages of

30

members of a running club.

Age, $a$ (years)	Frequency
$10 < a \le 20$	4
$20 < a \le 30$	9
$30 < a \le 40$	12
$40 < a \le 50$	5

(a) Calculate an estimate of the mean age. [3]

(b) Explain why your answer to part (a) is only an estimate. [1]

●●●●●Level 24 marksStart

The table shows information about the masses of

50

tomatoes.

Mass ( $m$ grams)	Frequency
$40 < m \le 50$	$6$
$50 < m \le 60$	$11$
$60 < m \le 70$	$17$
$70 < m \le 80$	$10$
$80 < m \le 90$	$6$

Draw a frequency polygon for this information.(2 marks)

●●●●●Level 22 marksStart

The table shows information about the lengths,

x

cm, of 50 leaves collected from a tree.

Length, $x$ (cm)	Frequency
$0 < x \le 10$	8
$10 < x \le 20$	14
$20 < x \le 30$	18
$30 < x \le 40$	10

Work out an estimate for the mean length of a leaf.

●●●●●Level 34 marksStart

30 shoppers each bought something from a market stall. The table shows information about the amount, £

a

, each shopper spent.

Amount spent, £ $a$	Frequency
$0 < a \le 5$	7
$5 < a \le 10$	12
$10 < a \le 15$	8
$15 < a \le 20$	3

(a) Write down the modal class.

(b) Work out an estimate for the mean amount spent by a shopper. Give your answer in pounds, correct to the nearest penny.

●●●●●Level 35 marksStart

A post office weighed 60 parcels. The table shows information about the weight,

w

grams, of each parcel.

Weight, $w$ (grams)	Frequency
$0 < w \le 50$	22
$50 < w \le 100$	19
$100 < w \le 150$	11
$150 < w \le 200$	8

(a) Work out an estimate for the mean weight of a parcel. Give your answer correct to 1 decimal place.

(b) Explain why your answer to part (a) can only be an estimate.

●●●●●Level 35 marksStart

The table shows the times,

t

minutes, that

30

people waited at a clinic.

Time, $t$ (minutes)	Frequency
$0 < t \le 20$	6
$20 < t \le 40$	11
$40 < t \le 60$	9
$60 < t \le 80$	4

(a) Work out an estimate for the mean waiting time. Give your answer correct to 1 decimal place. (3 marks)

(b) Write down the modal class. (1 mark)

●●●●●Level 34 marksStart

The table shows information about the time,

t

minutes, that each of

20

students spent on homework one evening.

Time, $t$ (minutes)	Frequency
$0 < t \le 10$	4
$10 < t \le 20$	6
$20 < t \le 30$	8
$30 < t \le 40$	2

(a) Work out an estimate for the mean time spent on homework. (3 marks)
(b) Write down the modal class. (1 mark)

●●●●●Level 34 marksStart

The table shows information about the amount, £

m

, spent by each of 50 customers in a shop.

Amount spent, £ $m$	Frequency
$0 < m \le 10$	12
$10 < m \le 20$	20
$20 < m \le 30$	13
$30 < m \le 60$	5

(a) Work out an estimate for the mean amount spent by a customer.

(b) The manager checks the till and finds that each of the 5 customers in the last class actually spent less than £40.

Explain what this tells you about your estimate in part (a).

●●●●●Level 45 marksStart

The table shows information about the lengths,

c

minutes, of 90 phone calls made from an office.

Length, $c$ (minutes)	Frequency
$0 < c \le 5$	24
$5 < c \le 10$	31
$10 < c \le 15$	20
$15 < c \le 20$	15

(a) Find the class interval that contains the median.

(b) Work out an estimate for the mean length of a call. Give your answer correct to 1 decimal place.

(c) Sam says that the median must be exactly the midpoint of the class interval found in part (a).

Explain why Sam is wrong.

●●●●●Level 47 marksStart

The table shows information about the time,

t

minutes, that each member of a gym class spent on a rowing machine. The frequency of one class is unknown.

Time, $t$ (minutes)	Frequency
$0 < t \le 10$	6
$10 < t \le 20$	$x$
$20 < t \le 30$	10
$30 < t \le 40$	4

An estimate for the mean time is 18 minutes.

(a) Work out the value of

x

.

(b) Find the class interval that contains the median.

●●●●●Level 56 marksStart

Two farms record the mass,

m

grams, of every egg they collect one morning.

Farm A collected 100 eggs.

Mass, $m$ (grams)	Frequency
$40 < m \le 50$	12
$50 < m \le 60$	38
$60 < m \le 70$	34
$70 < m \le 80$	16

Farm B collected 80 eggs.

Mass, $m$ (grams)	Frequency
$40 < m \le 50$	9
$50 < m \le 60$	21
$60 < m \le 70$	32
$70 < m \le 80$	18

(a) Work out an estimate for the mean mass of an egg from Farm A.

(b) Work out an estimate for the mean mass of all 180 eggs from the two farms together. Give your answer correct to 1 decimal place.

(c) A worker at Farm B says: "Our modal class is

60 < m \le 70

, so most of our eggs weigh 65 g."

Write down two things that are wrong with what the worker says.

●●●●●Level 58 marksStart

The cumulative frequency diagram shows the battery life, in hours, of 120 mobile phones.(a) Use the diagram to work out the frequency for each of the classes

0 < t \le 2

2 < t \le 4

4 < t \le 6

6 < t \le 8

and

8 < t \le 10

.

(b) Work out an estimate for the mean battery life.

●●●●●Level 55 marksStart