IGCSEMaths: ExtendedCIEExam Questions4. Probability & Statistics4.4 Averages & Range

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First teaching 2021

Last exams 2024

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Averages & Range (CIE IGCSE Maths: Extended)

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4.4 Averages & Range

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4.4 Averages & Range

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1
Sme Calculator1 mark

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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2
Sme Calculator6 marks

The test scores of 14 students are shown below.

21 21 23 26 25 21 22 20 21 23 23 27 24 21

Find the range, mode, median and mean of the test scores.
 

Range = ....................................................     
Mode = ....................................................     
Median = ....................................................     
Mean = ....................................................      

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3
Sme Calculator6 marks

Roberto records the value of each of the coins he has at home.
The table shows the results.

Value (cents) 1 2 5 10 20 50
Frequency 3 1 3 2 4 2
i)
Find the range.

........................................... cents [1]

ii)
Find the mode.

........................................... cents [1]

iii)
Find the median.

........................................... cents [1]

iv)
Work out the total value of Roberto’s coins.

........................................... cents [2]

v)
Work out the mean.

........................................... cents [1]

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4
Sme Calculator5 marks

A teacher records the number of days each of the 24 students in her class are absent.
The frequency table shows the results.

Number of days 0 1 2 3 4 5
Frequency 10 8 3 2 0 1


Find the mode, the median and the mean.

Mode = ...............................................     
Median = ...............................................     
Mean = ...............................................     

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5
Sme Calculator1 mark

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 Calculator4 marks

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

Calculate an estimate of the mean height.


............................................. m

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2
Sme Calculator4 marks

The speed, v km/h, of each of 200 cars passing a building is measured. 
The table shows the results.

Speed (v km/h) 0 less than v less or equal than 20 20 less than v less or equal than 40 40 less than v less or equal than 45 45 less than v less or equal than 50 50 less than v less or equal than 60 60 less than v less or equal than 80
Frequency 16 34 62 58 26 4

Calculate an estimate of the mean.
 

 ........................................ km/h

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3
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The table shows the marks scored by some students in a test.

Mark 5 6 7 8 9 10
Frequency 8 2 12 2 0 1


Calculate the mean mark.

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4
Sme Calculator4 marks

The table shows the time, t seconds, taken by each of 120 boys to solve a puzzle.

Time (t seconds) 20 less than t less or equal than 30 30 less than t less or equal than 35 35 less than t less or equal than 40 40 less than t less or equal than 60 60 less than t less or equal than 100
Frequency 38 27 21 16 18

Calculate an estimate of the mean time.
 

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

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5
Sme Calculator4 marks

20 students each record the mass, p grams, of their pencil case.
The table below shows the results.

Mass
(p grams)		 0 less than p less or equal than 50 50 less than p less or equal than 100 100 less than p less or equal than 125 125 less than p less or equal than 150 150 less than p less or equal than 200
Frequency 2 5 4 6 3

Calculate an estimate of the mean mass.
 

................................................ g

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6
Sme Calculator4 marks

A school nurse records the height, h cm, of each of 180 children.
The table shows the information.

Height (h cm) 60 less than h less or equal than 70 70 less than h less or equal than 90 90 less than h less or equal than 100 100 less than h less or equal than 110 110 less than h less or equal than 115 115 less than h less or equal than 125
Frequency 8 26 35 67 28 16


Calculate an estimate of the mean.
Give your answer correct to 1 decimal place.
 

.......................................... cm

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7
Sme Calculator4 marks

The table shows the amount of time, T minutes, 120 people each spend in a supermarket one Saturday.

Time (T minutes) Number of people
10 less than T less or equal than 30 16
30 less than T less or equal than 40 18
40 less than T less or equal than 45 22
45 less than T less or equal than 50 40
50 less than T less or equal than 60 21
60 less than T less or equal than 70 3

Use the midpoints of the intervals to calculate an estimate of the mean.

 

......................................... min

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8
Sme Calculator6 marks

A factory recycles metal.
The mass, x tonnes, of metal is measured each week.
The table shows the results for 52 weeks.

Mass (x tonnes) 100 less than x less or equal than 200 200 less than x less or equal than 250 250 less than x less or equal than 300 300 less than x less or equal than 500
Frequency 8 20 12 12

Calculate an estimate of the mean.


....................................... tonnes

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9a
Sme Calculator1 mark

The time taken for each of 120 students to complete a cooking challenge is shown in the table.

 Time (t minutes) 20 less than t less or equal than 25 25 less than t less or equal than 30 30 less than t less or equal than 35 35 less than t less or equal than 40 40 less than t less or equal than 45
 Frequency 44 32 28 12 4

Write down the modal time interval.


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

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9b
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Write down the interval containing the median time.


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

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9c
Sme Calculator4 marks

Calculate an estimate of the mean time.


......................................... min

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10
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The information below summarises data regarding the heights of plants, measured in centimetres.

Height, h cm 0 space less than space h space less or equal than space 10 10 space less than space h space less or equal than space 20 20 space less than space h space less or equal than space 30 30 space less than space h space less or equal than space 50
Frequency 2 18 62 38

Calculate an estimate of the mean height.

............................................ cm

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1
Sme Calculator4 marks

200 students estimate the total area, A space straight m squared, of the windows in the classroom.
The table shows their results.

Area (Am2) 20 space less than space A space less or equal than space 60 60 space less than space A space less or equal than space 100 100 space less than space A space less or equal than space 150 150 space less than space A space less or equal than space 250
Frequency 32 64 80 24


Calculate an estimate of the mean.
You must show all your working.
  

.......................................... m2 

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2
Sme Calculator4 marks

The frequency table shows the times, t minutes, each of 100 children spent exercising in one week.

Time (t minutes) 0 space less than space t space less or equal than space 60 60 space less than space t space less or equal than space 100 100 space less than space t space less or equal than space 160 160 space less than space t space less or equal than space 220 220 space less than space t space less or equal than space 320
Frequency 41 24 23 8 4

Calculate an estimate of the mean time.

.......................................... min

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3
Sme Calculator3 marks

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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4
Sme Calculator4 marks

Three sizes of eggs are sold in a shop.
The table shows the number of eggs of each size sold in one day.

Size Small Medium Large
Mass (m grams) 46 less than m less or equal than 52 52 less than m less or equal than 62 62 less than m less or equal than 80
Number of eggs sold 78 180 162

Calculate an estimate of the mean mass.

............................................. g

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5
Sme Calculator5 marks

The frequency table shows information about the number of books read by some students in a reading marathon.

Number of books read 1 2 3 4 5 6 7 8
Frequency 2 2 16 10 9 4 x 2
i)
The mean number of books read is 4.28.
 
Find the value of x.
 

x equals.................................................. [3]

ii)
Write down the mode.
 

[1]

iii)
Write down the median.
 

[1]

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6
Sme Calculator4 marks

During one year the midday temperatures, t°C, in Zedford were recorded.
The table shows the results.

Temperature (t°C) 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 25 25 less than t less or equal than 35
Number of days 50 85 100 120 10

Calculate an estimate of the mean.
 

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

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7
Sme Calculator4 marks

The frequency table shows information about the time, m minutes, that each of 160 people spend in a library.

Time (m minutes) 0 less than m less or equal than 10 10 less than m less or equal than 40 40 less than m less or equal than 60 60 less than m less or equal than 90 90 less than m less or equal than 100 100 less than m less or equal than 120
Frequency 3 39 43 55 11 9

Calculate an estimate of the mean time spent in the library.
 

......................................... min

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8
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100 students were each asked how much money, $ m, they spent in one week.
The frequency table shows the results.

Amount left parenthesis $ m right parenthesis 0 less than m less or equal than 5 5 less than m less or equal than 10 10 less than m less or equal than 20 20 less than m less or equal than 30 30 less than m less or equal than 50
Frequency 16 38 30 9 7

Calculate an estimate of the mean. 
 

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

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