Plotting Graphs from Data – scales, line of best fit, interpolation and extrapolation

What it shows

A graph turns a table of measurements into a visible pattern. The four data sets follow real laws – Hooke's law up to the elastic limit, exponential cooling, Ohm's law and steady plant growth – plus random error and one misread value. A good scale spreads the points over most of the grid. The line of best fit shows the trend and averages out random error, but anomalous results should be excluded first. Its gradient and intercept have a physical meaning. Reading between measured points is interpolation; reading beyond them is extrapolation, which assumes the pattern continues.

How to use

Choose a data set and a scale for each axis, then in 1. Plot points tap the grid for each row of the table. In 2. Best fit drag the orange handles, tap the anomalous point to exclude it and compare your line with Auto fit; for the cooling data switch Type: straight line to a curve. In 3. Read graph drag the cursor beyond the data and press Check by experiment.

Parameters you can change

• Data set Spring: extension vs load, Cooling water: temperature vs time, Resistor: current vs voltage, Seedling: height vs days
• Random measurement error 0–10 %
• Include one anomalous result (misreading)
• Starting fit type Depends on the data set, Straight line, Curve
• Points already plotted (untick so students plot them)

Questions to explore

1. Why should an anomalous result be excluded before drawing the line of best fit?
2. What does the gradient of the extension–load graph tell you about the spring?
3. Why is a value found by extrapolation less reliable than one found by interpolation?