Averages, Ranges & Data (OCR GCSE Maths: Higher): Exam Questions

3 hours55 questions
1
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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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2
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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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3
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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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4
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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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5
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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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6
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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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7
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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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8
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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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9
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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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10
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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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11
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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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12a
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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.

12b
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2 marks

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

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13a
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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

13b
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2 marks

Which class interval contains the median?

You must show your working.

13c
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2 marks

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

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14a
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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.

14b
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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.

14c
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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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15
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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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16
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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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17
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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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18
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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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19
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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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20
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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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21
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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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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