IGCSEMaths: ExtendedCIEExam QuestionsStatisticsAverages & Range

Syllabus Edition

First teaching 2023

First exams 2025

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Averages & Range (CIE IGCSE Maths: Extended)

Exam Questions

3 hours46 questions

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Averages & Range

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Averages & Range

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1a
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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

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1b
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Give a reason why the mean would be an unsuitable average to use.

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2
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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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3
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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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4
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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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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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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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7
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The heights, h metres, of the 120 boys in an athletics club are recorded.
The table shows information about the heights of the boys.

Height
(h metres)

 1.3 less than h less or equal than 1.4 1.4 less than h less or equal than 1.5 1.5 less than h less or equal than 1.6 1.6 less than h less or equal than 1.7 1.7 less than h less or equal than 1.8 1.8 less than h less or equal than 1.9
Frequency 7 18 30 24 27 14

Write down the modal class.


.................. less than h less or equal than ..................

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8
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The table gives information about the length of time, in minutes, that each of 60 students took to travel to school on Monday.

Length of time (bold italic t minutes) Frequency
0 space less than space t space less-than or slanted equal to space 10 4
10 space less than space t space less-than or slanted equal to space 20 10
20 space less than space t space less-than or slanted equal to space 30 15
30 space less than space t space less-than or slanted equal to space 40 25
40 space less than space t space less-than or slanted equal to space 50 6

Write down the modal class interval.

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1
Sme Calculator3 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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2
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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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3
Sme Calculator4 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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4
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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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The range, mode, median and mean of five positive integers are all equal to 10.

Find one possible set of these five integers.

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2
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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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3
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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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4
Sme Calculator3 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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5
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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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6
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Petra records the score in each test she takes.
 
The mean of the first n scores is x.
The mean of the first left parenthesis n minus 1 right parenthesis scores is left parenthesis x plus 1 right parenthesis.

Find the n text th end text score in terms of n and x.
Give your answer in its simplest form.

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