📈 Plot It Right! Mastering Scatter Diagrams & Correlation

Scatter diagrams may look like simple dot-plots, but they are a **powerful tool** for spotting relationships between two numerical variables. In O Level exams you will often be asked to comment on correlation, draw a line of best fit, or predict an unknown value. Mastering these skills not only scores easy marks but also sharpens your real-world data sense.

Understanding Correlation on a Scatter Diagram

When you plot paired data

(x, y)

as points, patterns emerge: **positive correlation** (points rise to the right), **negative correlation** (points fall to the right) or **no correlation** (points form no clear trend). The closer the dots cluster around an imagined straight line, the stronger the correlation. A line of best fit can then be sketched to summarise the trend and allow interpolation or limited extrapolation.

Worked Example – Height vs. Arm-span
Problem: A class recorded each student’s height

h

(cm) and arm-span

s

(cm). The scatter diagram suggests positive correlation. Estimate the arm-span of a student who is

170\,\text{cm}

tall.

Solution (step-by-step inside the diagram): 1) Draw a neat line of best fit through the cluster. 2) Locate

h = 170

on the horizontal axis. 3) Move vertically to the line, then horizontally to read

s \approx 171\,\text{cm}

. Hence the predicted arm-span is about

171\,\text{cm}

Key point 1: Correlation does NOT prove causation – it only shows association.
Key point 2: Keep axes evenly scaled so visual strength of correlation is not distorted.
Step 1 (example): Plot each $(h, s)$ pair clearly; label axes.
Step 2 (example): Sketch a thin, balanced line so roughly equal numbers of points lie on either side.

Practice by sketching scatter diagrams from past papers and asking yourself, “What kind of correlation is this? How strong is it? What prediction can I make?” With regular repetition you will quickly spot patterns and secure those straightforward exam marks!