Statistics Toolkit (AQA GCSE Maths)

Exam Questions

3 hours55 questions
1a
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2 marks

Naga states a hypothesis.

“Most people read more than 100 books a year.”

She asks a sample of five people in a book club how many books they read last month.
The table shows the results.

  Lynn Ali Paul Chen Ruth
Number of books 10 11 8 10 13

Show how Naga could use the data to support her hypothesis.

1b
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2 marks

Give two reasons why this sample should not be used to support her hypothesis.

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2a
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1 mark

In a sport, injury time is added time played at the end of a match.

The table shows the injury time, t (minutes) played in 380 matches.

Injury time, space t(minutes) Frequency
0 space less than space t space less-than or slanted equal to space 2 59
2 space less than space t space less-than or slanted equal to space 4 158
4 space less than space t space less-than or slanted equal to space 6 106
6 space less than space t space less-than or slanted equal to space 8 45
8 space less than space t space less-than or slanted equal to space 10 12

Circle the two words that describe the data.

continuous discrete grouped ungrouped

2b
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2 marks

Which class interval contains the median?

You must show your working.

2c
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2 marks

What percentage of the matches had more than 6 minutes of injury time?

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3a
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1 mark

Kim works at an airport in the UK.

She records the number of planes landing between 10 am and 2 pm each day.

The table shows the data for the first 10 days in January.

Day 1 2 3 4 5 6 7 8 9 10
Number of planes 148 151 147 155 153 147 155 102 151 154

The airport was affected by fog on one of the days.

Which day do you think it was?
Give a reason for your answer.

3b
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3 marks

Kim uses the data to predict how many planes will land at the airport in a year.

In her method, she

   uses an estimate of 150 planes in each 4-hour period throughout the day
   assumes the same number of planes each day.

Work out her prediction.

3c
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2 marks

In fact,

   fewer planes land in winter than in summer
   fewer planes land at night than during the day.

What does this tell you about Kim’s prediction?
Tick one box.

begin mathsize 26px style square end style Her prediction is too low

square Her prediction is too high

square Her prediction could be too low or too high

Give a reason for your answer.

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4
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1 mark

100 men and 100 women took a test.

Scores

  Median Interquartile range Range
Men 28 7.5 31
Women 30 9 37

Using this data, which statement must be true?
Tick one box.

begin mathsize 26px style square end style   Men had a higher average score than women

square   Men had more consistent scores than women

square   A woman had the highest score

square   A man had the lowest score

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5
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2 marks

In one month, the number of hours of exercise taken by 10 people are

4    7    2    8    6    5    1    82    3    9

Which is the appropriate average to use in this situation?
Tick a box.

begin mathsize 26px style square end style Mean       square Median       square Mode

Give one reason for each of the other two averages as to why they are not appropriate.

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6
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3 marks

Six positive numbers have

a mean of 10
a range of 19

Four of the numbers are    12    7    15    3

Work out the other two numbers.

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7
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1 mark

A station manager looks at the information below.

Number of
minutes late, bold italic t
Number of trains
0 space less-than or slanted equal to space t space less than space 2 12
2 space less-than or slanted equal to space t space less than space 4 0
4 space less-than or slanted equal to space t space less than space 6 7
6 space less-than or slanted equal to space t space less than space 8 0
8 space less-than or slanted equal to space t space less than space 10 0
10 space less-than or slanted equal to space t space less than space 12 1

Estimate the mean number of minutes late.

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8
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3 marks

The mean mass of a squad of 19 hockey players is 82 kg

A player of mass 93 kg joins the squad.

Work out the mean mass of the squad now.

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

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9
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4 marks

The table shows information about the times for 10 people to complete a task.

Time, t (minutes) Frequency
0 space less than space t space less-than or slanted equal to space 20 1
20 space less than space t space less-than or slanted equal to space 40 6
40 space less than space t space less-than or slanted equal to space 60 3

These statements are about the mean and range of the actual times.
Tick the correct box for each statement.

  True False
The mean could be less than 20 minutes begin mathsize 28px style square end style size 28px square
The mean could be more than 40 minutes size 28px square size 28px square
The mean could be less than 40 minutes size 28px square size 28px square
     
The range could be more than 40 minutes size 28px square size 28px square
The range could be less than 40 minutes size 28px square size 28px square
The range could be more than 60 minutes size 28px square size 28px square

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10
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2 marks

Students in a class took a spelling test.

The diagram shows information about the scores.

q11-paper1h-specimen2015-aqa-gcse-maths

Lucy is one of the 29 students in the class.

Her score was the same as the median score for her class.

Work out her score.

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11
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2 marks

15 people were asked how long, in minutes, they had been waiting for a bus.

Here are the results.

2 3 3 4 5 6 6 8 9 10 11 13 14 15 18

   

Find the interquartile range of these times.

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12
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2 marks

Here is the number of goals that Henri’s team scored one summer in each water polo match.

5    8    9    11    13    13    14    15    16    17    20

Find the interquartile range of the numbers of goals.
Show your working clearly.

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13
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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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14
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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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15
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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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16
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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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17
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1 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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18
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4 marks

15 students took an English test.
The same 15 students took a Maths test.
Both tests were marked out of 30.

For the English test results
the median was 21
the interquartile range was 14

The Maths test results are shown below.

18 18 19 20 24 25 25 26 28 28 29 29 29 30 30


Use the information above to compare the English test results with the Maths test results.
Write down two comparisons.

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19
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1 mark

Lee wishes to find out if there is a relationship between a person’s age and the time it takes them to complete a puzzle.

Lee decides to conduct an experiment.
She asks 12 people to complete the puzzle.
She records each person’s age and the time taken to complete the puzzle.

Make one criticism of Lee’s method.

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20
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3 marks

Ping chooses four numbers.

The mode of these four numbers is 8, the range is 7 and the mean is 11.

Find Ping’s four numbers.

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21
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4 marks

Jenny played four games of golf.
For these games her modal score was 76 and her mean score was 75.
Her range of scores was 10.

What were her scores for the four games?

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1
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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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2a
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1 mark

The table shows some information about the dress sizes of space 25 spacewomen.

Dress size Number of women
8 2
10 9
12 8
14 6

Find the median dress size.

2b
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1 mark

3 of the 25 women have a shoe size of 7
Zoe says that if you choose at random one of the 25 women, the probability that she has
either a shoe size of 7 spaceor a dress size of 14 is  9 over 25because

3 over 25 plus 6 over 25 equals 9 over 25

Is Zoe correct?
You must give a reason for your answer.

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3
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3 marks

The time-series graph gives some information about the number of pairs of shoes sold in a shoe shop in the first six months of 2014.

q4-easy-6-1-statistics-toolkit-edexcel-gcse-maths

The sales target for the first six months of 2014 was to sell a mean of 96 pairs of shoes per month.

Did the shoe shop meet this sales target?
You must show how you get your answer.

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4a
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2 marks

A bus company recorded the ages, in years, of the people on coach A and the people on coach B.

Here are the ages of the 23 people on coach A.

41 42 44 48 52 53 53 53 56 57 57 59
60 61 63 64 64 66 67 69 74 77 79  


Complete the table below to show information about the ages of the people on
coach A.

  Median  
  Lower Quartile  
  Upper Quartile  
  Least age 41
  Greatest age 79
4b
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1 mark

Here is some information about the ages of the people on coach B.

Median 70
Lower quartile 54
Upper quartile 73
Least age 42
Greatest age 85

Richard says that the people on coach A are younger than the people on coach B.

Is Richard correct?
You must give a reason for your answer.

4c
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1 mark

Richard says that the people on coach A vary more in age than the people on coach B.

Is Richard correct?
You must give a reason for your answer.

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5
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1 mark

Circle the expression for the range of n consecutive integers.

fraction numerator n plus 1 over denominator 2 end fraction n space – space 1 n n space plus space 1

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6
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1 mark

Here is some information about the times taken by 40 people to fill in a form.

Time, bold italic t minutes Number of people
0 space less than space t space less-than or slanted equal to space 5 3
5 space less than space t space less-than or slanted equal to space 10 9
10 space less than space t space less-than or slanted equal to space 15 11
15 space less than space t space less-than or slanted equal to space 20 17

In which class interval is the median?
Circle your answer.

0 space less than space t space less-than or slanted equal to space 5 5 space less than space t space less-than or slanted equal to space 10 10 space less than space t space less-than or slanted equal to space 15 15 space less than space t space less-than or slanted equal to space 20

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7
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3 marks

102 boys and 85 girls took a test.

The table shows information about the mean marks.

  Boys Girls
Number of students 102 85
Mean mark 68.5 72.4

The pass mark for the test was 70
Was the mean mark for all of these students greater than the pass mark?
You must show your working.

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8
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3 marks

Here is some information about 26 houses.

a comma space b and c are all different numbers.

Number of bedrooms Number of houses
1 7
2 a
3 b
4 c
5 8

The median number of bedrooms is 3.5

Work out a possible set of values for a comma space b and c.

a equals............................
b equals............................
c equals............................

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9
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3 marks

200 people recorded the time they spent on social media one day.

The table shows the results.

Time, t (mins) Frequency Midpoint  
0 space less-than or slanted equal to space t space less than space 30 24    
30 space less-than or slanted equal to space t space less than space 50 76    
50 space less-than or slanted equal to space t space less than space 60 52    
60 space less-than or slanted equal to space t space less than space 90 48    
  Total = 200    

Work out an estimate of the mean time.

..................................mins

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10
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3 marks

The table shows information about the distances walked by 120 students on their way to school one week.

Distance, bold italic x (miles) Frequency    
0 space less than space x space less-than or slanted equal to space 5 20    
5 space less than space x space less-than or slanted equal to space 10 48    
10 space less than space x space less-than or slanted equal to space 15 30    
15 space less than space x space less-than or slanted equal to space 20 22    
  Total = 120    

Work out an estimate for the mean distance.

...................miles

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11
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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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12
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3 marks

Diyar recorded the distance, in kilometres, that he cycled each day for 11 days.
Here are his results.

8 10 12 13 5 23 21 7 5 16 14

Find the interquartile range of his results.

....................................................... km

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13
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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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14
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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 attributes columnalign right center left columnspacing 0px end attributes row a equals cell.................. end cell row b equals cell.................. end cell row c equals cell.................. end cell end table

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15a
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3 marks

Sandeep sat 11 tests in January 2020
Each test was marked out of 60

Here are his test results.

45 space space space space space space 41 space space space space space space 35 space space space space space space space 44 space space space space space space space 38 space space space space space space 47 space space space space space space space 47 space space space space space space space 39 space space space space space space space 37 space space space space space space space 43 space space space space space space space 42

Find the interquartile range of these test results.
Show your working clearly.

15b
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1 mark

Sandeep also sat some tests in May 2020
Each test was marked out of 60

The median of the May 2020 test results is 42
The interquartile range of the May 2020 test results is 12

In which month, January or May, were Sandeep’s test results more consistent?
Give a reason for your answer.

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16a
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4 marks

A shop records the time taken by its customers to complete a purchase on its website.
The results from one day are summarised in this table.

Time taken
(t minutes)
Number of
customers
   
0 space less than space t space less-than or slanted equal to space 3 6    
3 less than space t space less-than or slanted equal to space 6 10    
6 space less than space t space less-than or slanted equal to space 9 6    
9 space less than space t space less-than or slanted equal to space 12 2    
12 space less than space t space less-than or slanted equal to space 15 1    

Calculate an estimate of the mean time taken.

....................... minutes

16b
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1 mark

Explain why it is not possible to use the information from this table to calculate the exact value of the mean time taken. 

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17
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5 marks

The police record the speed of vehicles passing a speed checkpoint.
The speeds are recorded in the table below.

Speed (s mph) Number of
vehicles
   
0 space less than space s space less-than or slanted equal to 20 5    
20 space less than space s space less-than or slanted equal to 40 8    
40 space less than space s space less-than or slanted equal to 50 37    
50 space less than space s space less-than or slanted equal to 60 47    
60 space less than space s space less-than or slanted equal to 80 3    

i)
Calculate an estimate of the mean speed of the vehicles.

..................... mph [4]

ii)
Explain why it is not possible to use the information from this table to calculate the exact value of the mean speed.

[1]

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18a
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1 mark

Ceri records the time taken, t minutes, to travel to school for a sample of 168 students at her Academy.

Time taken
(bold italic t minutes)
Frequency
0 space less than space t space less-than or slanted equal to space 10 54
10 space less than space t space less-than or slanted equal to space 20 50
20 space less than space t space less-than or slanted equal to space 40 44
40 space less than space t space less-than or slanted equal to space 80 20

Ceri says

The longest time that any of these students took to travel to school was 80 minutes.

Is she correct?
Give a reason for your answer.

18b
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3 marks

Ceri also claims that 25% of all of the students at this Academy took more than 30 minutes to travel to school.

i)
Show how Ceri might have worked out her claim.

[2]

ii)
State one assumption that Ceri has made in making her claim.

[1]

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1
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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 11th game?

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2
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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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3
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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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4
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3 marks

There are 10 boys and 20 girls in a class.
The class has a test.

The mean mark for all the class is 60
The mean mark for the girls is 54

Work out the mean mark for the boys.

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5
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3 marks

Walkden Reds is a basketball team.

At the end of 11 games, their mean score was 33 points per game.
At the end of 10 games, their mean score was 2 points higher.

Jordan says,

   "Walkden Reds must have scored 13 points in their 11th game."

Is Jordan right?
You must show how you get your answer.

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6
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2 marks

Mr Brown gives his class a test.
The 10 girls in the class get a mean mark of 70%
The 15 boys in the class get a mean mark of 80%

Nick says that because the mean of 70 and 80 is 75 then the mean mark for the whole class in the test is 75%

Nick is not correct.
Is the correct mean mark less than or greater than 75%?
You must justify your answer.

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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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9
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4 marks

The table gives information about the heights of 50 spacetrees.

Height( bold italic h metres) Frequency
0 less than h less-than or slanted equal to 4 8
4 less than h less-than or slanted equal to 8 21
8 less than h less-than or slanted equal to 12 12
12 less than h less-than or slanted equal to 16 7
16 less than h less-than or slanted equal to 20 2

Work out an estimate for the mean height of the trees.

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10a
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1 mark

The table gives information about the heights of space 35 spacegirls.

Height(bold italic h metres) Frequency
1.30 less-than or slanted equal to h less than 1.40 11
1.40 less-than or slanted equal to h less than 1.50 9
1.50 less-than or slanted equal to h less than 1.60 7
1.60 less-than or slanted equal to h less than 1.70 6
1.70 less-than or slanted equal to h less than 1.80 2

Find the class interval that contains the median.

10b
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4 marks

Work out an estimate for the mean height.

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11a
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3 marks

The table shows information about the weekly earnings of 20 spacepeople who work in a shop.

Weekly earnings(bold £ bold italic x) Frequency
150 less than x less-than or slanted equal to 250 1
250 less than x less-than or slanted equal to 350 11
350 less than x less-than or slanted equal to 450 5
450 less than x less-than or slanted equal to 550 0
550 less than x less-than or slanted equal to 650 3

Work out an estimate for the mean of the weekly earnings.

11b
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1 mark

Nadiya says,

   "The mean may not be the best average to use to represent this information."

Do you agree with Nadiya?
You must justify your answer.

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12a
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1 mark

The table shows some information about the foot lengths of space 40 spaceadults.

Foot length(bold italic f cm) Number of adults
16 less-than or slanted equal to f less than 18 3
18 less-than or slanted equal to f less than 20 6
20 less-than or slanted equal to f less than 22 10
22 less-than or slanted equal to f less than 24 12
24 less-than or slanted equal to f less than 26 9

Write down the modal class interval.

12b
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3 marks

Calculate an estimate for the mean foot length.

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13a
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3 marks

Jenny works in a shop that sells belts.

The table shows information about the waist sizes of 50 spacecustomers who bought belts from the shop in May.

Belt size Waist( bold italic w inches)  Frequency
Small 28 less than w less-than or slanted equal to 32 24
Medium 32 less than w less or equal than 36 12
Large 36 less than w less or equal than 40 8
Extra Large 40 less than w less or equal than 44 6

Calculate an estimate for the mean waist size.

13b
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2 marks

Belts are made in sizes Small, Medium, Large and Extra Large.

Jenny needs to order more belts in June.
The modal size of belts sold is Small.

Jenny is going to order 3 over 4 of the belts in size Small.
The manager of the shop tells Jenny she should not order so many Small belts.

Who is correct, Jenny or the manager?
You must give a reason for your answer.

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14
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3 marks

Hannah is planning a day trip for 195 students.

She asks a sample of 30 students where they want to go.
Each student chooses one place.

The table shows information about her results.

Place Number of students
Theme Park 10
Theatre 5
Sports Centre 8
Seaside 7

i)
Work out how many of the 195 students you think will want to go to the Theme Park.

[2]
ii)
State any assumption you made and explain how this may affect your answer.
[1]

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15
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1 mark

25 students in class A did a science exam.
30 students in class B did the same science exam.

The mean mark for the 25 students in class A is 67.8
The mean mark for all the 55 students is 72.0

Work out the mean mark for the students in class B.                                         

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16
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4 marks

Here are two sets of numbers, A and B.

q11-paper-3h-june-2019-aqa-gcse-maths

mean of Set A : mean of Set B = 3 : 8

Work out the value of x.

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