Statistical Diagrams (Edexcel GCSE Maths)

Exam Questions

2 hours36 questions
1
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2 marks

The frequency table gives information about the heights of some people.

Height (bold italic h cm) Frequency
160 space less than space h space less-than or slanted equal to 165 2
165 space less than space h space less-than or slanted equal to 170 5
170 space less than space h space less-than or slanted equal to 175 10
175 space less than space h space less-than or slanted equal to 180 21
180 space less than space h space less-than or slanted equal to 185 16
185 space less than space h space less-than or slanted equal to 190 4

Draw a frequency polygon for this information.

q1-easy-6-2-statistical-diagrams-edexcel-gcse-maths

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2a
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1 mark

The table shows some information about the ages of space 60 spaceteachers.

Age( bold italic a years) Frequency
20 space less than a less-than or slanted equal to 30 6
30 space less than a less-than or slanted equal to 40 16
40 space less than a less-than or slanted equal to 50 14
50 space less than a less-than or slanted equal to 60 22
60 space less than a less-than or slanted equal to 70 2

Write down the modal class interval.

2b
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2 marks

Draw a frequency polygon for the information in the table.

q2b-easy-6-2-statistical-diagrams-edexcel-gcse-maths

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3a
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2 marks

The table gives information about the money, £A, some people spent on an internet site one day.

Money spent(£A) Frequency
0 less than A less-than or slanted equal to 20 10
20 less than A less-than or slanted equal to 40 15
40 less than A less-than or slanted equal to 60 25
60 less than A less-than or slanted equal to 80 40
80 less than A less-than or slanted equal to 100 6

On the grid, draw a frequency polygon for this information.

q3a-easy-6-2-statistical-diagrams-edexcel-gcse-maths
3b
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1 mark

Write down the modal class interval.

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4
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3 marks

Here are the times, in minutes, that 20 children took to walk to school.

13 21 19 27 31 5 23 29 18 25
34 15 28 23 22 40 16 19 32 9

Draw an ordered stem and leaf diagram for these times.

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5
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3 marks

Here are the heights, in cm, of 18 children.

98 90 84 102 115 91
88 91 108 110 97 93
90 89 103 95 92 106

Show this information in an ordered stem and leaf diagram.

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6
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3 marks

Here are the heights, in mm, of 20 plants.

53 44 48 56 48 64 51 33 41 44
31 52 55 63 60 56 47 61 37 56


Draw an ordered stem and leaf diagram for these heights.

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7
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3 marks

Sixteen babies are born in a hospital.

Here are the weights of the babies in kilograms.

2.4 2.7 3.5 4.4 4.5 4.1 4.4 2.8
4.1 3.8 3.8 4.2 3.3 3.0 3.7 3.3

Show this information in an ordered stem and leaf diagram.

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8
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3 marks

You must write down all stages in your working.

Here are the ages, in years, of 15 students.

19 18 20 25 37
33 21 17 29 20
42 18 23 37 22

Show this information in an ordered stem and leaf diagram.

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9
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3 marks

Here are the speeds, in miles per hour, of 16 cars.

31 52 43 49 36 35 33 29
54 43 44 46 42 39 55 48

Draw an ordered stem and leaf diagram for these speeds.

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10
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3 marks

Here are the lengths, in cm, of 15 tables.

28 51 42 23 63
38 44 29 32 37
61 35 39 41 25

Draw an ordered stem and leaf diagram for these lengths.

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11
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1 mark

The graph shows the cost of a litre of petrol for the last six months of 2017.

q3b-paper6-june2019-ocr-gcse-maths

Explain why this graph is misleading.

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12
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1 mark

This chart shows the types of dance performed by 12 dancers.
3 performed a street dance, 8 performed a jazz dance and 1 performed a tap dance.

q1c-paper6-nov2018-ocr-gcse-maths

Why is this diagram misleading?

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13
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1 mark

Percy sells paint in standard tins and large tins.
The standard tin covers 40m2 and the large tin covers 60m2.

Percy publishes this chart showing the area that can be covered with each tin of paint.

q18a-paper6-june2018-ocr-gcse-maths

Explain why the chart is misleading.

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14
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1 mark

The pie chart summarises information about the visitors to the tourist attraction on a single day.

q3b-paper6-june2017-ocr-gcse-maths

Explain why the pie chart cannot be used to work out how many adults visited on that day.

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15
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3 marks

There are only apple trees, cherry trees, pear trees and plum trees in an orchard.

The pictogram shows information about the numbers of apple trees, cherry trees and
pear trees in the orchard.

nov-2018-1ma1-1h-q7

There is a total of 30 trees in the orchard.

Complete the pictogram.

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1a
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2 marks

The frequency table gives information about the numbers of emails sent by space 51 spaceteachers on Monday.

Number of emails sent(bold italic m) Frequency
0 less than m less-than or slanted equal to 10 5
10 less than m less-than or slanted equal to 20 17
20 less than m less-than or slanted equal to 30 14
30 less than m less-than or slanted equal to 40 9
40 less than m less-than or slanted equal to 50 6

On the grid below, draw a frequency polygon for this information.

q1-medium-6-2-statistical-diagrams-edexcel-gcse-maths
1b
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2 marks

Nalini says that at least a quarter of these teachers sent more than space 30 spaceemails.

Is Nalini correct?
You must explain your answer.

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2a
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2 marks

The frequency table gives information about the times it took some office workers to get to the office one day.

Time(bold italic t minutes) Frequency
0 space less than t less-than or slanted equal to 10 4
10 space less than t less-than or slanted equal to 20 8
20 space less than t less-than or slanted equal to 30 14
30 space less than t less-than or slanted equal to 40 16
40 space less than t less-than or slanted equal to 50 6
50 space less than t less-than or slanted equal to 60 2

Draw a frequency polygon for this information.

q2a-medium-6-2-statistical-diagrams-edexcel-gcse-maths
2b
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1 mark

Write down the modal class interval.

2c
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2 marks

One of the office workers is chosen at random.

Work out the probability that this office worker took more than 40 minutes to get to the office.

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3a
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1 mark

The table shows information about the heights of space 80 spacechildren.

Height( bold italic h bold spacecm) Frequency
130 space less than h less-than or slanted equal to space 140 4
140 space less than h less-than or slanted equal to space 150 11
150 space less than h less-than or slanted equal to space 160 24
160 space less than h less-than or slanted equal to space 170 22
170 space less than h less-than or slanted equal to space 180 19

Find the class interval that contains the median.

3b
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2 marks

Draw a frequency polygon for the information in the table.

q3b-medium-6-2-statistical-diagrams-edexcel-gcse-maths

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4a
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1 mark

The grouped frequency table gives information about the heights of space 30 spacestudents.

Height( bold italic h bold spacecm) Frequency
130 space less than h less-than or slanted equal to space 140 1
140 space less than h less-than or slanted equal to space 150 7
150 space less than h less-than or slanted equal to space 160 8
160 space less than h less-than or slanted equal to space 170 10
170 space less than h less-than or slanted equal to space 180 4

Write down the modal class interval.

4b
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2 marks

This incorrect frequency polygon has been drawn for the information in the table.

q4b-medium-6-2-statistical-diagrams-edexcel-gcse-maths

Write down two things wrong with this incorrect frequency polygon.

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5a
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3 marks

Here are the heights in centimetres of 20 men.

165 164 176 179 188 178 183 172 180 190
167 159 156 176 173 168 169 182 167 192

Show this information in an ordered stem and leaf diagram.

5b
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2 marks

Work out the percentage of these men with a height greater than 184 cm.

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6a
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3 marks

Chloe recorded the test marks of 20 students.

22 29 38 16 36 18 30 21 27 43
14 41 25 38 46 19 48 34 23 46

Show this information in an ordered stem and leaf diagram.

6b
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2 marks

One of these students is going to be chosen at random.

Find the probability that this student has a test mark less than 28

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7a
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1 mark

The table shows information about the heights of space 80 spaceplants.

Height( bold italic h cm) Frequency
10 less than h less-than or slanted equal to 20 7
20 less than h less-than or slanted equal to 30 13
30 less than h less-than or slanted equal to 40 14
40 less than h less-than or slanted equal to 50 12
50 less than h less-than or slanted equal to 60 16
60 less than h less-than or slanted equal to 70 18

Find the class interval that contains the median.

7b
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2 marks

On the grid, draw a frequency polygon for the information in the table.

q7b-medium-6-2-statistical-diagrams-edexcel-gcse-maths

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8
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2 marks

Sean has drawn a time series graph to show the numbers, in thousands, of visitors to a fun park.

q8-medium-6-2-statistical-diagrams-edexcel-gcse-maths

Write down two things that are wrong or could be misleading with this graph.

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9a
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1 mark

The time series graph shows information about the percentages of the people in a village that used the village shop for the years between 1980 and 2010.

q9a-medium-6-2-statistical-diagrams-edexcel-gcse-maths

Describe the trend in the percentage of the people in the village who used the shop for this period.

9b
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2 marks
i)
Use the graph to predict the percentage of the people in the village likely to use the shop in the year 2020.

[1]
ii)
Is your prediction reliable?
Explain your answer.
[1]

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10
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3 marks

The table gives some information about the birds Paula sees in her garden one day.

Bird Frequency
Magpie 15
Thrush 10
Startling 20
Sparrow 27


Complete the accurate pie chart.

q10-medium-6-2-statistical-diagrams-edexcel-gcse-maths

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11a
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2 marks

A music festival has taken place each year from 2011

The table shows the number of people who attended each year.

  Year 2011 2012 2013 2014 2015 2016 2017 2018
  Number of people 350 583 906 1471 2023 2612 3251 3780

The festival organisers draw a time series graph to represent the data.
The first four years have been plotted.

q6-paper-3h-nov-2018-aqa-gcse-maths

Complete the graph.

11b
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2 marks

Use the graph to estimate the number of people who will attend the festival in 2019.

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12
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3 marks

The pie chart shows information about voters in an election.

q10-paper2h-june2017-aqa-gcse-maths

3360 more women voted than men.

Work out the total number of voters.

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13a
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2 marks

The time students spent watching TV was recorded.

The table shows the average daily time per student each year from 2012 to 2019

Year 2012 2013 2014 2015 2016 2017 2018 2019
Time (minutes) 157 148 138 124 113 100 90 82


A time series graph is drawn to represent the data.
The first four points have been plotted.

q5-paper-2h-nov-2020-aqa-gcse-maths

Complete the graph.

13b
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1 mark

Use the graph to estimate the average daily time per student in 2020

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

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14a
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1 mark

The graph shows the number of umbrellas sold in Ling’s shop for each quarter from quarter 1 of 2017 to quarter 3 of 2019.

q9-paper4-nov2020-ocr-gcse-maths

The shop sold 32 umbrellas in quarter 4 of 2019.
Complete the graph.

14b
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1 mark

Make one comment about the seasonal variation shown in this graph.

14c
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1 mark

Make one comment about the annual variation shown in this graph.

14d
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1 mark

Ling predicts that she will sell 50 umbrellas in quarter 1 of 2020.

What assumption has she made?

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15a
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2 marks

The table shows the average number of customers per day entering a shop.

  2015 2016
Months Jan-
Mar
Apr-
Jun
July-
Sep
Oct-
Dec
Jan-
Mar
Apr-
Jun
July-
Sep
Oct-
Dec
Average number of
customers per day
119 264 368 172 130 304 381 192


Complete the time series graph below.

q8a-paper4-june2017-ocr-gcse-maths

15b
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2 marks

Make two different comments comparing the number of customers entering the shop in 2015 and 2016.

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1
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3 marks

The pie charts give information about the ages, in years, of people living in two towns, Adley and Bridford.

q1-1-hard-6-2-statistical-diagrams-edexcel-gcse-maths

q1-2-hard-6-2-statistical-diagrams-edexcel-gcse-maths

The ratio of the number of people living in Adley to the number of people living in Bridford is given by the ratio of the areas of the pie charts.

What proportion of the total number of people living in these two towns live in Adley and are aged 0 -19?
Give your answer correct to 3 significant figures.

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2
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3 marks

The pie chart shows information about people at a theme park.

q9-paper3h-nov2019-aqa-gcse-maths

There were 450 more women than men.

Work out the number of children.

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3a
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2 marks

Fran asks each of 40 students how many books they bought last year.

The chart below shows information about the number of books bought by each of the 40 students.

gcse-edexcel-2018-nov-p3-q4a

Work out the percentage of these students who bought 20 or more books.

 ...........%

3b
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1 mark

Show that an estimate for the mean number of books bought is 9.5
You must show all your working.

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4
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3 marks

The table shows information about the heights, in cm, of a group of Year 9 girls.
 

least height 150 cm
median 165 cm
greatest height 170 cm

This stem and leaf diagram shows information about the heights, in cm, of a group of 15 Year 9 boys.
 

1ma1-1h-q7 
Compare the distribution of the heights of the girls with the distribution of the heights of the boys.

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5a
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2 marks

The table shows the number of computers sold in Tom’s shop each quarter from 2015 to 2017.

  2015 2016 2017
Quarter 1 2 3 4 1 2 3 4 1 2 3 4
Number of
computers sold
13 31 29 45 20 32 25 47 27 40 30 58

Complete this graph using the information for 2017.

q8a-paper5-nov2018-ocr-gcse-maths

5b
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2 marks

Tom adds the three results for quarter 1 and he adds the three results for quarter 4.
Tom says

The ratio of the total number of computers sold in quarter 1 compared to quarter 4 is   2 : 5.

Is he correct?
Show your reasoning.

5c
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2 marks

Make two comments about Tom’s sales over the period 2015 to 2017.

5d
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1 mark

Tom predicts that he will sell more than 60 computers in the 4th quarter of 2018.

What assumption has he made?

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6a
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3 marks

John wants to investigate whether men in the UK are better at estimating a time interval of 10 seconds than women in the UK. He decides to sample the population by asking his work colleagues to take the test.

The diagrams below summarise John’s results.

q6-1-paper6-spec2015-ocr-gcse-maths

q6-2-paper6-spec2015-ocr-gcse-maths

What information from the diagrams can be used to support each of these statements?

i)
The older John’s colleagues are, the lower their estimate is.

[1]

ii)
Males in the sample tend to underestimate the interval and females in the sample tend to overestimate the interval.

[2]

6b
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2 marks

Comment on whether any conclusions can be drawn for the UK population from the results of this sample. 

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