Scatter diagrams

Maths · Statistics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A scatter diagram shows two measurements for each person or item as one point, for example height on one axis and mass on the other. The pattern of the points shows whether the two quantities are linked. This link is called correlation.

If the points lie close to a straight line, you can draw a line of best fit with a ruler. It follows the trend of the points, with about the same number of points on each side. It does not have to pass through the origin or through any of the points.

The line is used to estimate one value from the other. An estimate is reliable only inside the range of the data.

Rules to remember

Positive correlation: as one quantity increases, the other increases (points slope upwards from left to right).
Negative correlation: as one quantity increases, the other decreases (points slope downwards from left to right).
Zero (no) correlation: the points show no pattern.
The closer the points are to a straight line, the stronger the correlation.
Line of best fit: one straight ruled line through the middle of the points, with points balanced on both sides.
An outlier is a point far from the pattern of the others.
Estimates outside the range of the data are unreliable, because the trend may not continue.

Common mistake

Joining the points one by one, or forcing the line of best fit through the origin or through the first and last points. Draw one straight line that follows the trend of all the points.

Worked example

A scatter diagram shows the age of cars, x years, and their value, y thousand dollars. The ages are from 2 to 10 years. The line of best fit passes through (2, 30) and (10, 14). Estimate the value of a car that is 7 years old.

Gradient = (14 − 30) ÷ (10 − 2) = −16 ÷ 8 = −2.
From (2, 30) to x = 7 is an increase of 5 in x, so y changes by −2 × 5 = −10.
y = 30 − 10 = 20. (7 years is inside the range 2 to 10, so the estimate is reliable.)

Answer: About 20 thousand dollars

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