Syllabus Edition

First teaching 2021

Last exams 2024

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Averages & Range (CIE IGCSE Maths: Extended)

Exam Questions

3 hours44 questions
1a
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1 mark

The mass, correct to the nearest kilogram, of each of 11 parcels is shown below.


24,   23,   23,   26,   25,   27,   18,   96,   16,   17,   32


Find the mode.

............................................... kg

1b
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1 mark

Give a reason why the mean would be an unsuitable average to use.

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2
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1 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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3
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1 mark

The time, t minutes, it takes each of 50 students to travel to school is recorded.
The table shows the results.

Time (t minutes) 0 less than t less or equal than 10 10 less than t less or equal than 15 15 less than t less or equal than 20 20 less than t less or equal than 40
Frequency 7 19  16 8


Write down the modal class.

................ less than t less or equal than ................ min

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4
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2 marks

Twenty students took a Science test and a Maths test.

Both tests were marked out of 50

The table gives information about their results.

  Median Interquartile range
Science 27 18
Maths 24.5 11

Use this information to compare the Science test results with the Maths test results.
Write down two comparisons.

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5
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1 mark

The table shows information about the weights, in kg, of 40 parcels.

Weight of parcel ( p kg) Frequency
0 space less than space p space less-than or slanted equal to space 1 19
1 space less than space p space less-than or slanted equal to space 2 12
2 space less than space p space less-than or slanted equal to space 3 5
3 less than space space p space less-than or slanted equal to space 4 2
4 space less than space p less-than or slanted equal to space 5 2

Write down the modal class.

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6
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3 marks

The students in Class A and in Class B take the same examination.

The lowest score in Class A is 39
The range of scores for Class A is 57
The lowest score in Class B is 33
The range of scores for Class B is 60

Find the range of scores for all the students in both classes.

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7
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1 mark

The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.

Speed
(s kilometres per hour)
Frequency
40 space less than space s space less-than or slanted equal to space 50 10
50 space less than space s space less-than or slanted equal to space 60 16
60 space less than space s space less-than or slanted equal to space 70 19
70 space less than space s space less-than or slanted equal to space 80 23
80 space less than space s space less-than or slanted equal to space 90 12

Write down the modal class.

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1
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3 marks

The table shows the marks scored by 40 students in a test.

Mark 5 6 7 8 9 10
Frequency 8 5 11 7 5 4


Calculate the mean mark.

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2a
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1 mark

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

Find the mode.

2b
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3 marks

Calculate the mean.

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3
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3 marks

Ed has 4 cards.
There is a number on each card.

12   6   15   ?

The mean of the 4 numbers on Ed's cards is 10
Work out the number on the 4th card.

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4
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3 marks

Jenny has six cards.

Each card has a whole number written on it so that

the smallest number is 5
the largest number is 24
the median of the six numbers is 14
the mode of the six numbers is 8

Jenny arranges her cards so that the numbers are in order of size.

q5-january-2022-1h-edexcel-igcse-maths

For the remaining four cards, write on each dotted line a number that could be on the card.

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5
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4 marks

Yusuf sat 8 examinations.
Here are his marks for 5 of the examinations.

68  72  75  77  80


For his results in all 8 examinations

the mode of his marks is 80
the median of his marks is 74
the range of his marks is 16

Find Yusuf’s marks for each of the other 3 examinations.

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6
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4 marks

Given that  a space less than space b space less than space c
the four whole numbers a comma space a comma space b and c have

a mode of 7
a median of 8.5
a mean of 9

Work out the value of a, the value of b and the value of c.

table row a equals cell.................. end cell row b equals cell.................. end cell row c equals cell.................. space end cell end table

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1
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4 marks

The table shows information about the times, t seconds, taken by each of 100 students to solve a puzzle.

Time (t s) 0 less than t less or equal than 10 10 less than t less or equal than 15 15 less than t less or equal than 20 20 less than t less or equal than 40 40 less than t less or equal than 75
Frequency 9 18 22 30 21

Calculate an estimate of the mean time.
 

............................................... s

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2
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4 marks

The table shows the amount of money, $ x, given to a charity by each of 60 people.

Amount ($ x) 0 less than x less or equal than 20 20 less than x less or equal than 25 25 less than x less or equal than 35 35 less than x less or equal than 50 50 less than x less or equal than 100
Frequency 21 16 6 10 7

 
Calculate an estimate of the mean.
 

$................................................

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3
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3 marks

5 n is the mean of the three numbers 391, n and n minus 1.

Find the value of n.


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

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4
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3 marks

Hertford Juniors is a basketball team.

At the end of 10 games, their mean score is 35 points per game.
At the end of 11 games, their mean score has gone down to 33 points per game.

How many points did the team score in the 11 th game?

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5
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3 marks

There are 18 packets of sweets and 12 boxes of sweets in a carton.

The mean number of sweets in all the 30 packets and boxes is 14
The mean number of sweets in the 18 packets is 10

Work out the mean number of sweets in the boxes.

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6
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3 marks

There are 15 children at a birthday party.

The mean age of the 15 children is 7 years.

9 of the 15 children are boys.
The mean age of the boys is 5 years.

Work out the mean age of the girls.

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7
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4 marks

Bob asked each of 40 spacefriends how many minutes they took to get to work.
The table shows some information about his results.

Time taken (m minutes) Frequency
0 less than m less-than or slanted equal to 10 3
10 less than m less-than or slanted equal to 20 8
20 less than m less-than or slanted equal to 30 11
30 less than m less-than or slanted equal to 40 9
40 less than m less-than or slanted equal to 50 9


Work out an estimate for the mean time taken.

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8
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4 marks

Sumeet records the times, in minutes, for 40 runners to finish a half marathon.
Information about these times is shown in the table.

Time (bold italic t minutes) Frequency
60 less than t less-than or slanted equal to 90 10
90 less than t less-than or slanted equal to 120 14
120 less than t less-than or slanted equal to 150 9
150 less than t less-than or slanted equal to 180 5
180 less than t less-than or slanted equal to 210 2

Calculate an estimate for the mean time.

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