Level 3MathsAQAMathematical Studies (Core Maths)Paper 1: Data, Finance, Estimation & ModellingExam QuestionsAnalysis of DataRepresenting Data Numerically

Representing Data Numerically (AQA Level 3 Mathematical Studies (Core Maths): Paper 1: Data, Finance, Estimation & Modelling): Exam Questions

Exam code: 1350

1 hour7 questions
1a
4 marks

  • The World Health Organisation (WHO) collects data about life expectancy.

  • The WHO estimates the average life expectancy at birth for a person born in a particular country.

The data below are for 193 countries.

Life expectancy at birth (l years)

Number of countries

45 less-than or slanted equal to l less than 50

12

50 less-than or slanted equal to l less than 60

24

60 less-than or slanted equal to l less than 70

44

70 less-than or slanted equal to l less than 75

53

75 less-than or slanted equal to l less than 80

32

80 less-than or slanted equal to l less than 85

28

The life expectancy at birth for a person in the UK is 77 years. A newspaper headline said:

UK in top 40 countries for life expectancy

Use the given data to comment on the newspaper’s headline.

You may use the grid if you wish.

Square grid paper featuring evenly spaced, light blue horizontal and vertical lines forming small squares, suitable for drawing or plotting data.

How did you do?

1b
4 marks

For the whole world, the WHO gives the mean life expectancy at birth as 68.5 years.

The table below shows the life expectancy at birth sorted by world region and gender.

Life expectancy at birth

Region

Female

Male

Africa

61.0

57.9

Americas

77.7

71.9

Eastern Mediterranean

72.1

68.3

Europe

80.1

74.0

South-East Asia

72.2

68.2

Western Pacific

75.8

71.1

Compare the life expectancy by region and gender, commenting on any trends.

Compare the mean life expectancy given by WHO with the data in the table.

Consider whether region or gender has a greater effect on life expectancy.

How did you do?

1c
6 marks

  • The World Health Organisation (WHO) collects data about life expectancy.

  • The WHO estimates the average life expectancy at birth for a person born in a particular country.

Estimate how far a person is likely to walk in their lifetime.

Show details of your assumptions and calculations.

How did you do?

2
5 marks

30 students from School A and 30 students from School B took part in a Maths challenge.

Each student completed as many maths puzzles as possible in an hour.

The table shows the results for School A.

Number of puzzles

Frequency

4

1

5

7

6

12

7

8

8

2

Total = 30

Here is some information about the results for School B

Mean number of puzzles

5.3

Standard deviation

0.87

Compare the performance of the two schools.

Show working to support your comparisons

How did you do?

3a
1 mark

Mr Berry wants his class to study some data on swimming times.

He collects data from the Internet about two swimming strokes, backstroke and breaststroke.

The table shows the fastest 19 times, in seconds, for the men’s 100m Backstroke at a major championship.

Swimmer

A

B

C

D

E

F

G

H

I

J

Time (s)

51.85

51.94

52.38

52.54

52.91

52.98

53.17

53.45

53.60

53.86

Swimmer

K

L

M

N

O

P

Q

R

S

Time (s)

53.93

54.51

54.91

54.95

55.00

55.16

55.17

55.19

55.38

Which two words describe the type of data he has collected?

Tick(✓) your answers.

  • qualitative

  • primary

  • quantitative

  • secondary

Choose your answer

3b
3 marks

The table below shows information about the fastest 19 times for the men’s 100m Breaststroke in the same championship.

Lowest value

Lower quartile

Median

Upper quartile

Highest value

Breaststroke

49.45

50.12

51.76

52.32

53.44

Backstroke

51.85

55.38

Complete this table to show the information for the backstroke.

The lowest and highest values have been completed for you.

How did you do?

3c
3 marks

Draw box and whisker plots to represent the data for the backstroke and breaststroke times.

A blank graph grid with vertical and horizontal lines labelled with time in seconds from 49 to 55.5 on the x-axis; y-axis unlabelled.

How did you do?

3d
2 marks

Make two comparisons of the distribution of times for the swimming strokes.

You should make one comparison based on the averages and one comparison based on the spreads.

How did you do?

4a
3 marks

15 students sat a Maths exam and an English exam.

Both exams were marked out of 30

The stem-and-leaf diagram shows their Maths marks.

Maths marks

Key 1 | 8 represents a mark of 18

0 | 5 7

1 | 1 3 9 9

2 | 1 2 4 7 7 8 9 9

3 | 0

The table shows information about their English marks.

Lowest value

Lower quartile

Median

Upper quartile

Highest value

English marks

3

17

19

26

28

Maths marks

Complete the table to show the information for the Maths exam.

How did you do?

4b
3 marks

Draw box and whisker plots to represent the data for the English and Maths exams.

Blank graph paper with horizontal axis labelled "Marks" ranging from 0 to 35. The chart features a grid of small squares.

How did you do?

4c
1 mark

Compare the average marks for the English and Maths exams.

How did you do?

4d
1 mark

Which marks were more consistent, English or Maths?

Give a reason for your answer.

How did you do?

5a
4 marks

Linda grows and sells potatoes.

The mean mass of her potatoes in last year’s crop was 193 grams.

She sees this advert for a new fertiliser for potatoes.

New potato fertiliser advertisement claiming to increase crop mass by at least 15%, featuring bold text and a starburst with "New!".

Linda uses the fertiliser on her next crop of potatoes.

The table shows the mass of these 130 potatoes when she picks them.

Mass, m grams

Number of potatoes

120 space less or equal than m less than 160

12

160 space less or equal than m less than 200

23

200 space less or equal than m less than 240

45

240 space less or equal than m less than 280

32

280 space less or equal than m less than 320

18

Based on these two crops of potatoes, is the claim in the advert justified? You must show your working.

How did you do?

5b
4 marks

Dan also grows and sells potatoes.

The histogram shows the distribution of the masses of his potatoes this year.

Histogram of mass in grams showing frequency density. Bars range from 120 to 320 grams, peaking between 180 and 220 grams.

The potatoes are classed as small, medium and large.

Medium potatoes have a mass between 188 grams and 260 grams.

Estimate the number of Dan’s potatoes that are classed as medium.

How did you do?

6a
4 marks

A report has claimed that, due to streaming, modern technology is responsible for reducing the length of song introductions (intros).

Steven collected data from two different time periods, 1970 to 2000 and 2010 to 2018, to test this claim.

Length of intro in seconds

1970 to 2000

2010 to 2018

120

20

78

10

65

14

65

18

52

9

32

22

50

23

20

12

68

6

41

14

39

19

56

15

72

10

59

15

61

16

87

23

48

15

62

21

27

28

Complete the table below to show the summary statistics for 1970 to 2000

Lowest value

Lower quartile

Median

Upper quartile

Highest value

1970 to 2000

2010 to 2018

6

12

15

21

28

How did you do?

6b
3 marks

Draw box and whisker plots on the grid below to represent the two sets of data.

Graph with a labelled x-axis showing "Length of intro in seconds" from 0 to 120, y-axis unlabelled, and a grid background; no data points.

How did you do?

6c
2 marks

Make two comparisons of the lengths of song intros from the two sets of data.

How did you do?

7a
1 mark

The boys from class 10A did a cross-country run.

Here are their times in minutes.

24.6

22.3

29.2

36.4

31.3

35.0

25.4

34.5

42.0

39.6

19.5

What was the median time in minutes?

  • 22.5

  • 30.9

  • 31.3

  • 35.0

Choose your answer

7b
2 marks

Work out the interquartile range of the times for the boys from class 10A.

How did you do?

7c
4 marks

The rest of the year 10 boys in the school also did the cross-country run.

The box and whisker diagram shows the distribution of their times.

Box plot showing data range from 17 to 41 minutes, with quartiles at 20, 31, and 36 minutes. Grid background with horizontal time axis.

Compare the performance of the boys in class 10A with the rest of the year 10 boys.

How did you do?