Scatter Graphs
A scatter graph is a diagram that plots pairs of data values as points, used to show whether there is a relationship, or correlation, between two variables. It appears in GCSE statistics, where students describe positive, negative or no correlation, spot outliers, and draw a line of best fit to estimate unknown values.
Method
- Plot each pair of data as a point on the grid, using the x-value for the first variable and the y-value for the second.
- Look at the overall pattern of the points to decide the type of correlation: positive (both increase together), negative (one increases as the other decreases), or no correlation (no pattern).
- Identify any outliers, points that do not fit the general trend, and consider whether to include them when judging the correlation.
- Draw a line of best fit through the data: a straight line that follows the trend with roughly equal numbers of points above and below it.
- Use the line of best fit to read off an estimate for a value of one variable given the other.
- Check whether your estimate is interpolation (within the range of the data) or extrapolation (outside it), since extrapolated estimates are unreliable.
Worked example
A gardener records the height of a plant (cm) against the number of days since planting. A line of best fit has been drawn through the points (10, 20) and (30, 100). Use the line of best fit to estimate the height of the plant after 15 days.
- Find the gradient of the line of best fit: gradient = (100 - 20) / (30 - 10) = 80/20 = 4.
- Write the equation relating height (y) to days (x) starting from the point (10, 20): y = 20 + 4 x (x - 10).
- Substitute x = 15 into the equation: y = 20 + 4 x (15 - 10) = 20 + 4 x 5.
- Work out the value: y = 20 + 20 = 40.
- State the final answer: the estimated height after 15 days is 40 cm. Since 15 days is within the range of days used to draw the line, this is a reliable interpolation.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
A student records the number of visitors to a park and the daily rainfall (mm). As rainfall increases, the number of visitors tends to decrease. State the type of correlation this shows, and describe what it means in context.
A scatter graph plots the number of weeks since a seedling was planted against its height in cm for 8 readings. A line of best fit has been drawn through the points (2, 10) and (12, 60). (a) Find the gradient of the line of best fit. (1) (b) Use the line to estimate the height of the seedling after 9 weeks. (2)
A scientist records the number of hours of sunlight (0 to 12 hours) and the growth of a plant in mm each week, and finds a strong positive correlation. A line of best fit is used to estimate the growth for a week with 20 hours of sunlight. (a) State whether this estimate is reliable, and explain your answer. (2) (b) Explain why correlation between sunlight and growth does not necessarily mean sunlight is the only cause of the growth, giving one other possible factor. (2)
See real past-paper questions on scatter graphs, organised by topic with official mark schemes →
Free printable worksheet
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