Write down the type of correlation you would expect to see in a scatter graph of each of the following.
The daily temperature and the number of ice creams sold at a kiosk.
The age of a car and its value.
2 marks
Show answer
a) positive correlationb) negative correlation
2
The table shows the age and the value of six second-hand cars of the same model.
Age (years)
1
2
3
5
6
8
Value (£1000s)
12
10.5
9
7
6
3.5
A scatter graph is drawn of value against age. Describe the type of correlation.
1 mark
Show answer
negative correlation
3
The table shows the number of hours that each of 8 students spent revising, and their scores in a test.
Hours revising
1
2
3
4
5
6
7
8
Test score
22
28
35
39
47
52
58
65
The data is plotted on a scatter graph.
Describe the type of correlation the scatter graph would show.
Interpret this correlation for these students.
2 marks
Show answer
a) positive correlationb) Students who spent longer revising scored higher marks
4
The table shows the hours seven students spent revising and their test scores.
Hours
1
2
3
4
5
6
7
Score
25
35
48
52
66
70
85
On the grid, plot these points to make a scatter graph.
2 marks
Show answer
Seven points plotted correctly
5
The table shows the hours of sunshine and the number of ice creams a kiosk sold on seven days.
Hours of sunshine
2
3
4
5
6
7
8
Ice creams sold
30
42
50
22
71
80
92
One day does not fit the pattern. Write down the hours of sunshine and the ice creams sold on that day.
Ignoring that day, describe the correlation.
2 marks
Show answer
a) (5, 22)b) positive correlation
6
A garage records the engine size, in litres, and the top speed of a number of cars. The engine sizes range from 1.0 litres to 2.5 litres. A scatter graph of the data shows strong positive correlation and a line of best fit has been drawn.
Priya uses the line of best fit to estimate the top speed of a car with a 4.5 litre engine. Explain why her estimate may not be reliable.
Dev says, "The graph proves that a bigger engine causes a higher top speed." Give one reason why Dev may be wrong.
2 marks
Show answer
(a) 4.5 litres is outside the range of the data (1.0 to 2.5 litres), so this is extrapolation and the trend may not continue. (b) Correlation does not prove causation; another factor (e.g. car weight or design) could affect top speed.
7
A scatter graph of children aged 5 to 11 shows positive correlation between shoe size and score on a reading test.
Sam says, "Bigger feet make you better at reading." Explain why Sam is wrong.
2 marks
Show answer
Correlation does not mean cause. Both depend on age: older children have bigger feet and read better.
8
The table shows the midday temperature and the number of hot chocolates a café sold on seven days.
Temperature (°C)
2
5
8
11
14
17
20
Hot chocolates
64
55
46
60
28
19
10
The line of best fit has equation y = 70 − 3x, where x is the temperature and y is the number of hot chocolates.
Write down the outlier.
Describe the correlation.
Use the line of best fit to estimate the number sold when the temperature is 10°C.
3 marks
Show answer
a) (11, 60)b) negative correlationc) 40
9
A line of best fit on a scatter graph passes through the points (2, 10) and (8, 34).
Use the line to estimate the value of y when x = 5.
2 marks
Show answer
22
10
The scatter graph shows the number of hours of sunshine and the number of visitors to a country park on each of 10 days.
Describe the correlation shown by the scatter graph.
On another day there were 7.5 hours of sunshine. By drawing a line of best fit, estimate the number of visitors to the park on this day.
3 marks
Show answer
a) positive correlationb) approximately 160 (accept 150-175)
11
A shop records the temperature (from 12°C to 28°C) and the number of cold drinks sold each day. The line of best fit has equation y = 4x + 10, where x is the temperature in °C and y is the number of drinks.
Estimate the number of drinks sold when the temperature is 20°C.
Write down what the gradient of 4 tells you.
Kim uses the line to predict sales on a day when the temperature is 40°C. Explain why her prediction may not be reliable.
4 marks
Show answer
a) 90b) 4 extra drinks sold for every 1 degree rise in temperaturec) 40 degrees is outside the range of the data (12 to 28), so the line may not continue
12
The table shows the maths score and the science score of 8 students.
Maths score
10
20
25
30
35
40
45
50
Science score
18
26
32
38
40
44
50
54
The first six points have been plotted on the scatter graph.
Complete the scatter graph by plotting the last two points.
Describe the correlation between the maths scores and the science scores.
Interpret this correlation.
3 marks
Show answer
a) (45,50) and (50,54) plotted correctlyb) positive correlationc) The higher a student's maths score, the higher their science score tends to be
13
A factory records the age, in years, and the weekly maintenance cost, in pounds, of its machines. A scatter graph of the data is drawn and a line of best fit passes through the points (1, 20) and (9, 60).
What type of correlation does the graph show?
Use the line of best fit to find an estimate for the weekly maintenance cost of a machine that is 5 years old.
3 marks
Show answer
a) positive correlationb) £40
14
The scatter graph shows the outside temperature, in °C, and the number of portions of soup sold by a cafe on each of 8 days.
One of the points is an outlier. Write down the coordinates of this point.
Ignoring the outlier, use the graph to estimate the number of portions of soup sold on a day when the outside temperature is 9 °C.
3 marks
Show answer
a) (11, 10)b) approximately 47 (accept 44-50)
15
The scatter graph shows the number of hours each of 9 students spent revising and their scores in an exam marked out of 80.
Write down the type of correlation shown.
Draw a line of best fit on the scatter graph.
Use your line of best fit to estimate the exam score of a student who revised for 5.5 hours.
Amir revised for 20 hours. Explain why the line of best fit should not be used to estimate his score.
4 marks
Show answer
a) positive correlationb) a straight line following the trend of the pointsc) approximately 53 (accept 49-57)d) 20 hours is outside the range of the data (0 to 9 hours), so the trend may not continue
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.