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Averages & Range (Cambridge O Level Maths)

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Averages & Range

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1
Sme Calculator3 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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2
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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3
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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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 Calculator4 marks

The table shows the distances travelled by 80 people to a shopping mall.

Distance (d km) 0 space less than space d space less-than or slanted equal to space 5 5 space less than space d space less-than or slanted equal to space 10 10 space less than space d space less-than or slanted equal to space 20 20 space less than space d space less-than or slanted equal to space 50
Frequency 35 20 14 11

Calculate an estimate of the mean distance travelled.

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6a
Sme Calculator1 mark

A survey recorded the number of people living in each of 50 houses.
The bar chart shows the results.

q2-june-2021-4024-21-cambridge-o-level-maths-d

Find the mode.

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6b
Sme Calculator1 mark

Find the median

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6c
Sme Calculator3 marks

Calculate the mean.

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1
Sme Calculator3 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
Sme Calculator1 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 6 6 6 7 3 6 2

Find the mode.

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2b
Sme Calculator3 marks

Calculate the mean.

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3
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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4
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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5
Sme Calculator3 marks

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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6
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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7
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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8
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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9
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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10
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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11a
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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11b
Sme Calculator1 mark

Write down the interval containing the median time.


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

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11c
Sme Calculator4 marks

Calculate an estimate of the mean time.


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

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12
Sme Calculator4 marks

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

The height, h cm, of each of 100 students is measured.
The table shows the results.

Height (h cm) 100 < h ⩽ 150 150 < h ⩽ 160 160 < h ⩽ 165 165 < h ⩽ 185
Frequency 7 30 41 22

Calculate an estimate of the mean.

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

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2
Sme Calculator4 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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3
Sme Calculator4 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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4
Sme Calculator4 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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5
Sme Calculator4 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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6
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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7
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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8
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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9
Sme Calculator4 marks

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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10
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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11
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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12
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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13
Sme Calculator5 marks

The times taken by the 80 students to complete a Science test are shown in the frequency table.

Time (m minutes) 40 less than m less-than or slanted equal to 50 50 less than m less-than or slanted equal to 60 60 less than m less-than or slanted equal to 70 70 less than m less-than or slanted equal to 80 80 less than m less-than or slanted equal to 90
Frequency 8 13 p 20 q


An estimate for the mean time taken to complete the test is 67.625 minutes.
This is calculated using the mid-interval value as an estimate of the time in each interval.

 Calculate the value of p and the value of q.

p = .................. q = .................

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