Scatter Diagrams & Correlation (Edexcel GCSE Statistics: Foundation): Exam Questions

Exam code: 1ST0

29 mins4 questions
1a
2 marks

This question must be answered with a cross in a box ☒. If you change your mind about an answer, put a line through the box ☒ and then mark your new answer with a cross ☒.

Raina has been watching the judging of a cake baking competition.

Two judges ranked the 10 bakers for their sponge cakes.

Raina calculated the Spearman's rank correlation coefficient for the ranks given by the judges.

She got a value of 0.8.

(i) What type of correlation is shown by the value 0.8? Put a cross in one of the boxes below.

Negative correlation ☐      No correlation ☐      Positive correlation

(ii) Interpret Raina’s value.

1b
1 mark

The same two judges will also be judging a flower-arranging competition.

Is it possible to say anything about the ranks they are likely to give for flower arranging based on the value of Spearman's rank correlation coefficient that Raina calculated?

Give a reason for your answer.

2a
1 mark

The maximum temperature (°C) and the number of hours of sunshine were recorded in Sheffield each day in July for 11 successive years.

For each July, the mean maximum temperature and the total number of hours of sunshine were calculated.

The scatter diagram shows this information.

Scatter graph showing correlation between mean maximum temperature in Celsius and total hours of sunshine, ranging from 150 to 300 hours.

In one of these years there was a total of 244 hours of sunshine in July.

For this year, write down the mean maximum temperature.

................................. °C

2b
1 mark

For the year with the lowest total number of hours of sunshine in July, write down the mean maximum temperature.

................................. °C

2c
1 mark

Draw a line of best fit on the scatter diagram.

2d
3 marks

Describe and interpret the type of correlation shown by the scatter diagram.

2e
2 marks

For a different year in Sheffield, there was a total of 220 hours of sunshine in July.

(i) Estimate the mean maximum temperature for July that year.

................................. °C

(ii) Give a reason why your answer to part (e)(i) should be reliable.

3a
1 mark

Timur is investigating the heights and weights of rugby players. He collected data from the internet about the heights and weights of players from the Wales rugby squad.

The players from the Wales rugby squad are classed as Forwards or Backs.
Timur draws a scatter diagram for the heights and weights of some of the Backs from the Wales rugby squad.

Scatter plot shows weight versus height of individuals, ranging from 170 to 205 cm and 75 to 110 kg, with data points scattered throughout.

Explain why a scatter diagram is appropriate for the type of data Timur collected.

3b
2 marks

The data for three of the players was not plotted on the scatter diagram.
The height and weight of each of these players is given in the table below.

Player

A

B

C

Height (cm)

183

183

173

Weight (kg)

95

87

78

Complete the scatter diagram by plotting the points for players A, B and C.

3c
2 marks

Describe and interpret the type of correlation shown by the scatter diagram.

3d
2 marks

The double mean point for the heights and weights of all of the Backs is (184, 92).

Draw a line of best fit through the double mean point.

3e
1 mark

Timur also collected the heights and weights of players from the England rugby squad. He found the Spearman’s rank correlation coefficient for the heights and weights of the Forwards from the England rugby squad.

The correlation coefficient was 0.00

Interpret this correlation coefficient in context.

3f
2 marks

Timur used statistical software to find the following information about the heights (x cm) and weights (y kg) of the Backs from the Wales rugby squad and the Backs from the England rugby squad.

Spearman's rank correlation coefficient

Gradient of line of best fit

Wales rugby squad Backs

0.81

0.96

England rugby squad Backs

0.65

1.02

(Source: www.englandrugby.com (opens in a new tab))

Compare the Spearman's rank correlation coefficients and interpret this comparison in the context of the question.

3g
2 marks

Timur uses the information in the table to conclude that the weight of the England rugby squad Backs increases faster than the weight of the Wales rugby squad Backs as their height increases.

Assess the validity of Timur’s conclusion with reference to the statistical results.

4a
2 marks

Jim is investigating the relationship between air temperature and altitude.

He has found data on the internet showing the average air temperature at different altitudes on one particular day.

The table shows the results he collected.

Altitude (metres)

0

1000

2000

3000

4000

5000

6000

8000

10 000

Average air temperature (°C)

15.0

8.5

2.0

−4.5

−11.0

−17.5

−24.0

−36.9

−49.9

He uses this information to draw the scatter diagram.

Graph showing average air temperature in degrees Celsius decreasing with increasing altitude in metres, from 0°C at 2000m to -55°C at 12000m.

Describe and interpret the correlation shown in the scatter diagram

4b
1 mark

Draw a line of best fit on the scatter diagram.

4c
1 mark

Use the scatter diagram and your line of best fit to predict the average air temperature at an altitude of 4400 metres.

4d
2 marks

Jim wants to predict the average air temperature at an altitude of 11000 metres.

Discuss whether or not it is appropriate to use the line of best fit to make his prediction.