IGCSEMaths: CoreCIEExam QuestionsStatisticsAverages & Range

Syllabus Edition

First teaching 2021

Last exams 2024

|

Averages & Range (CIE IGCSE Maths: Core)

Exam Questions

2 hours27 questions
Easy
Medium
Hard
1
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Here are the weekly wages, in dollars, of the ten workers in an office.

280 200 175 1180 95 182 238 256 194 250
i)
Find the median.

$ ................................................. [2]

ii)
Calculate the mean.
$ ................................................. [2]
iii)
For this office, explain why the mean is not a suitable average.
[1]

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2
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The table shows the maximum power, kW, and the time taken, in seconds, to accelerate from 0 to 100 km/h for each of 10 cars.

Maximum
power (kW)		 77 52 103 55 44 51 85 135 90 110
Time
(seconds)		 12.5 14.9 9.0 12.1 14.4 12.9 10.0 7.1 11.0 9.4

i)
Find the range of the times.
........................................... s [1]
ii)
Find the median maximum power.
........................................... kW [2]

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3
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Dina has a set of 12 cards.
These are the numbers on the cards.

3 4 1 3 2 1 3 4 2 2 1 3

Work out

i)
the median,
[2]
ii)
the mode,
[1]
iii)
the mean,
[2]
iv)
the range.
[1]

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4a
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27 14 8 93 32 55 14 38 73 47

From this list of numbers find

the median,

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4b
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27 14 8 93 32 55 14 38 73 47

From this list of numbers find

the range.

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5a
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These are the number of texts sent one day by each of 10 students.

18 13 15 8 9 17 12 8 6 14

Write down the mode.

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5b
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Calculate the mean.

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6a
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Emma records the number of letters in each word in a sentence.

7 1 5 4 2 4 5 3 3 1 2 4

Find

i)
the median,
[2]
ii)
the mode,
[1]
iii)
the range.
[1]

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6b
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Jack records the number of letters in 25 words.

Number of
letters in a word		 Number of
words
1 3
2 1
3 5
4 8
5 6
6 2
i)
Calculate the mean.

[3]
ii)
Priti picks one of Jack’s words at random.

Find the probability that this word has 4 or more letters.
[2]

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7
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At Donville station the number of tickets sold each day is recorded for seven days.

104 18 72 31 27 45 60

Find

i)
the range,
[1]
ii)
the median,
[2]
iii)
the mean.
[2]

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8
Sme Calculator1 mark

The table shows the different methods of travel for 20 people going to work.

Method of travel Frequency
Car 10
Walk 5
Bike 3
Bus 2

Which type of average, mean, median or mode, can be used for this information?

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9a
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16        7        23        18       73       20        95        17       89       54

For this list of numbers, find

the median,

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9b
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the range.

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10
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The number of melons sold in a shop each day for 7 days is shown below.

18          5           23           40           28           19           17

Work out the mean number of melons sold.

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11a
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Monday Tuesday Wednesday Thursday Friday Saturday
67 75 53 68 94 87

The table shows the number of customers in a restaurant on each day it is open during one week.

Write down the day most customers came into the restaurant.

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11b
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Calculate the mean number of customers per day.

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11c
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Find the range of the number of customers.

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12
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Geoff keeps a record of the number of goals scored in the first eight games played by his football team.

3              1              8              5              7              2              1              6

Find

i)
the mode,

[1]

ii)
the range,
[1]
iii)
the median.
[2]

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1
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The table shows the temperature, in °C, at midday on the first day of each month during one year in a city.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
9 11 15 19 23.5 27.5 29 28 25 19.5 14.5 10

Calculate the mean of these temperatures.

............................................. °C 

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2
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Helena has a set of cards.
She takes one card at random and records the number shown.
She does this 50 times.
The results are shown in the table.

Number on card Frequency
1 8
2 11
3 10
4 9
5 12

Calculate the mean of her results.

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3
Sme Calculator7 marks

Joel spins a fair five-sided spinner numbered 2, 3, 4, 5 and 6.

The table shows the results of his first 20 spins.

Number 2 3 4 5 6
Frequency 3 2 6 4 5

i)
Write down the mode.
[1]
ii)
Calculate the mean.
[3]

Joel wants to draw a pie chart to show the results in the table.

iiia)
Show that the sector angle for the number 2 is 54°.
[1]
iiib)
Find the sector angle for the number 6.
[2]

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4
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The table shows the number of bananas bought by the last 50 customers at a store.

Number of
bananas bought		 Frequency
0 14
1 0
2 2
3 5
4 11
5 8
6 10
i)
Find the range.
[1]
ii)
Work out the median.
[1]
iii)
Calculate the mean.
[3]

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5
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The number of people in each of 150 cars entering a leisure centre car park is recorded.
The table shows the results.

Number of people 1 2 3 4 5
Frequency 44 43 30 25 8

i)
Write down the mode.

[1]

ii)
Calculate the mean.

[3]

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6
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The table shows the number of pets owned by each of the 95 students in a school.

Number of pets Frequency
0 5
1 14
2 39
3 14
4 23

Calculate the mean number of pets.

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7
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40 people were asked how many times they visited the cinema in one month.
The table shows the results.

Number of cinema visits 0 1 2 3 4 5 6 7
Frequency 5 5 6 6 7 3 6 2

i)
Find the mode.

[1]

ii)
Calculate the mean.
[3]

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8
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The table shows the number of goals scored by Geoff’s team in each game during one season.

Number of goals 0 1 2 3 4 5 6 7 8
Number of games 5 7 8 10 6 4 5 3 2

i)
How many games did the team play?

[1]

ii)
Work out the mean number of goals scored per game.

[3]

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1
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Ning has a spinner numbered 1 to 6.
She spins it 50 times and her results are shown in the table.

Number on
spinner		 Frequency
1 15
2 12
3 9
4 5
5 2
6 7

i)
Write down the mode.
[1]
ii)
Find the median.
[1]
iii)
Work out the mean.
[3]

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2
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The mean of seven numbers is 16.

Six of these numbers are 12, 20, 19, 10, 21 and 13.

Find the seventh number.

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3
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Six students bring an apple to school one day.
The list shows the mass of each apple, correct to the nearest gram.

82 94 78 103 88 82

Find

ia)
the mode,
.............................................. g [1]
ib)
the range,
.............................................. g [1]
ic)
the median.
.............................................. g [2]
ii)
Another student, Toni, also brings an apple to school.
The mean mass of the 7 apples is 89g.

Work out the mass of Toni’s apple.
.............................................. g [3]

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4
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The mean of three numbers is 150.

The numbers are 361, 2n and open parentheses n minus 1 close parentheses .

Find the value of n.

n = ................................................... 

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5
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Five numbers have a mean of 9.4 .
Four of the numbers are 3, 5, 10 and 12.

Work out the range of the five numbers.

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6
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70 people each attempt a driving test.
Each person repeats the test until they pass.
The results are shown in the table.

Number of attempts Number of people
1 19
2 17
3 8
4 12
5 9
6 5

i)
Write down the mode.

[1]

ii)
Calculate the mean.

[3]

iii)
Jules says that the median is 3.5.

Show that he is wrong.
[1]

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7
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The number of examinations that each of the 196 candidates takes is recorded in the table.

Number of examinations 5 6 7 8
Number of candidates 27 42 63 64

i)
Write down the range.
[1]
ii)
Find the median.

[1]

iii)
Calculate the mean.

[3]

iv)
A candidate is selected at random.

Find the probability that the candidate takes fewer than 8 examinations.
[2]

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