IGCSE · Practice questions · Scatter diagrams and correlation

Spot the trend.

Six original Cambridge-style questions on scatter diagrams, correlation and lines of best fit.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Describe, draw, then estimate inside the data.

Plot small crosses; never join them.
Describe the correlation (positive, negative, zero; strong or weak) and say what it means in context.
Draw one ruled line across the data, near the mean point, with points evenly on each side.
Estimate by reading up and across from the line.
Judge: estimates outside the data are unreliable; correlation is not cause.

Recall

[3 marks]

State the type of correlation you would expect between

(a) the outside temperature and the cost of heating a house (b) the length of a person's foot and their height (c) a person's house number and their mass.

(a) negative (warmer days, less heating) ✓
(b) positive ✓
(c) zero (no correlation) ✓

Calculation

[3 marks]

Hours of revision \(x\) and test mark \(y\) for 8 students:

\(x\): 1, 2, 3, 4, 5, 6, 7, 8 \(y\): 31, 40, 41, 50, 52, 61, 63, 70

(a) Calculate the mean point. (b) Describe the correlation.

(a) \(\bar{x} = \dfrac{36}{8} = 4.5\) and \(\bar{y} = \dfrac{408}{8} = 51\), so the mean point is (4.5, 51). ✓
(b) Strong positive correlation: students who revised for longer tended to score higher marks. ✓

Calculation

[3 marks]

For the data in the previous question, a line of best fit passes through (2, 38) and (8, 68).

(a) Use the line to estimate the mark for 5 hours of revision. (b) Estimate the hours of revision for a mark of 60.

The line rises \(68 - 38 = 30\) marks over 6 hours, so 5 marks per hour. ✓
(a) \(38 + 3 \times 5 = 53\) marks. ✓
(b) 60 is \(60 - 38 = 22\) marks above (2, 38), which is \(22 \div 5 = 4.4\) hours further, so about 6.4 hours. ✓

Analysis

[2 marks]

A student uses the same line to predict the mark for 15 hours of revision. Give two reasons why this prediction is unreliable.

15 hours is outside the range of the data (1 to 8 hours), so the trend may not continue. ✓
The line gives \(38 + 13 \times 5 = 103\) marks, which is more than a test out of 100 allows. ✓

Analysis

[2 marks]

The heights (cm) and masses (kg) of 7 students are (150, 45), (155, 49), (160, 52), (165, 30), (170, 61), (175, 64), (180, 70). Identify the outlier and say whether it should be used when drawing the line of best fit.

The other points rise by about 4 kg every 5 cm, so about 57 kg is expected at 165 cm. (165, 30) is far below the pattern: it is the outlier. ✓
It may be a recording error, so ignore it when drawing the line of best fit. ✓

Analysis

[4 marks]

A town council finds strong positive correlation between the number of fire engines sent to a fire and the cost of the damage. A councillor says: 'Sending fewer fire engines would reduce the damage.'

(a) What does the positive correlation mean in context? (b) Explain why the councillor is wrong.

(a) Fires that had more fire engines sent tended to cause more damage. ✓
(b) Correlation does not show cause. ✓
A third factor, the size of the fire, explains both: big fires need more engines AND cause more damage. ✓
Sending fewer engines would probably make the damage worse, not better. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.