GCSEMaths: FoundationEdexcelExam QuestionsStatisticsStatistics Toolkit

Statistics Toolkit (Edexcel GCSE Maths: Foundation)

Exam Questions

2 hours28 questions
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1
Sme Calculator2 marks

Sophie wants to find out how often people go to the cinema.

She gives a questionnaire to all the women leaving a cinema.

Her sample is biased.

State two possible reasons why.

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2
Sme Calculator3 marks

The table below shows the number of goals a team scored in 46 matches.

Goals Scored Frequency
0 7
1 18
2 13
3 6
4 2
5 or more 0

Find the mean number of goals scored per match.

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3
Sme Calculator5 marks

James and Susan are playing a game where points are scored.

Their points for 6 attempts at the game are shown below.

James 4 4 6 5 7 3
Susan 1 8 9 10 2 3

 

(i)

Who had the most consistent score?
Give a reason for your answer.

[2]

(ii)

Who had the highest mean score over the 6 attempts?
You must show your working.

[3]

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4
Sme Calculator5 marks

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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5
Sme Calculator3 marks

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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6
Sme Calculator6 marks

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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7a
Sme Calculator2 marks
27 14 8 93 32 55 14 38 73 47

From this list of numbers find

the median,

[2]

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7b
Sme Calculator1 mark
27 14 8 93 32 55 14 38 73 47

From this list of numbers find

the range.

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8a
Sme Calculator1 mark

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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8b
Sme Calculator2 marks

Calculate the mean.

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9a
Sme Calculator4 marks

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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9b
Sme Calculator5 marks

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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10
Sme Calculator1 mark

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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11
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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1
Sme Calculator3 marks

A factory which produces bicycles is planning to make four different models; A, B, C, and D.

60 people are asked which of the four models they would be most likely to buy.

The table shows information about the results.

Bicycle Model Number of people
A 17
B 11
C 24
D 8

 
The factory is going to make 20 000 bicycles next year.

(i)

Work out how many model C bicycles the factory should make next year.

[2]

(ii)

Explain why your answer to part (i) may be inaccurate.

[1]

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2
Sme Calculator1 mark

The table below shows the number of goals a team scored in 45 matches.

Goals Scored Frequency
0 7
1 18
2 13
3 6
4 1
5 or more 0

Find the median number of goals scored per game.

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3
Sme Calculator4 marks

Daniel asked 50 students how many minutes they each took to get to school.

Time taken
(t minutes)		 Frequency    
0 < t  ≤ 10 8    
10 < t  ≤ 20 21    
20 < t  ≤ 30 11    
30 < t  ≤ 40 10    

 

Work out an estimate for the mean number of minutes taken by the 50 students.

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4
Sme Calculator2 marks

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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5
Sme Calculator3 marks

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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6
Sme Calculator7 marks

Joel spins a fair five sides spinner numbered 2, 3, 4, 5, 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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7
Sme Calculator3 marks

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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8
Sme Calculator4 marks

The number of people in each of 150 cars entering the 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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1
Sme Calculator6 marks

Ken wants to find investigate the opinion of students in his school, which has 5 year groups.

The table gives information about the number of students in each year group in Ken's school.

Year group Number of students
First year 170
Second year 162
Third year 155
Fourth year 168
Fifth year 140

 

(i)

State the population in this situation.

[1]

(ii)

State one reason why Ken should consider surveying a sample.

[1]

(iii)

State one reason why Ken should consider surveying the population.

[1]

(iv)

Ken decides to take a survey of 30 students.

Calculate how many students from Fifth year should be in his sample for it to be representative of the population.

[3]

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2
Sme Calculator2 marks

The table shows information about the number of hours that 110 children spent playing video games last week.

Number of hours (h) Frequency
0 < h  ≤ 2 12
2 < h  ≤ 4 15
4 < h  ≤ 6 28
6 < h  ≤ 8 30
8 < h  ≤ 10 20
10 < h  ≤ 12 5

 

Jamie is trying to calculate an estimate for the mean number of hours that the 110 children played video games for last week.

His working is shown below.

Number of hours (h) Frequency Midpoint Frequency × Midpoint
0 < h  ≤ 2 12 1 12
2 < h  ≤ 4 15 3 45
4 < h  ≤ 6 28 5 140
6 < h  ≤ 8 30 7 210
8 < h  ≤ 10 20 9 180
10 < h  ≤ 12 5 11 55
Total 110 36 642

 

Mean = italic 642 over italic 36 italic equals italic 17 italic. italic 8 italic space h r s

 

Jamie has made 1 mistake in his calculation.

Describe the mistake and correct it to find the correct estimated value of the mean.

[2]

 

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3
Sme Calculator7 marks

The table gives information about the weights, in kg, of 36 packages being loaded on to a delivery truck.

Weight (w kg) Frequency
0 < w  ≤ 10 12
10 < w  ≤ 15 14
15 < w  ≤ 20 7
20 < w  ≤ 35 3

 

(i)

Calculate an estimate for the mean weight of the packages.

[4]

 

(ii)

Explain why your answer to part (i) will only be an estimate.

[1]

 

(iii)

On a different delivery truck, there are 50 packages.

Using the data in the table, estimate the number of these packages that weigh between 0 and 10 kg.

[2]

 

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4
Sme Calculator5 marks

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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5
Sme Calculator2 marks

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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6
Sme Calculator2 marks

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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7
Sme Calculator3 marks

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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8
Sme Calculator4 marks

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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9
Sme Calculator7 marks

The number of examinations that each of 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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