Statistics — A Complete Guide

Statistics is one of the easier topics to score on if you're systematic. The arithmetic is straightforward; the marks come from picking the right calculation for the question and presenting your work clearly. This guide covers averages and spread, frequency tables (ungrouped and grouped), and the four diagrams that appear regularly across GCSE papers.

The three averages — and when to use which

• Mean — sum of all values divided by the count. Good when data is fairly evenly distributed; affected by outliers.
• Median — the middle value when data is in order. Best when there are extreme outliers.
• Mode — the most frequent value. The only average that works for non-numerical data (e.g. favourite colour).

Range — the simplest measure of spread

Useful but easily distorted by a single outlier. The IQR is more robust (see the cumulative frequency guide).

Frequency tables (ungrouped data)

Grouped data — the estimated mean

When the data is in classes (e.g. 10 < h ≤ 20), you don't know the exact values, so you estimate the mean using the midpoint of each class.

Modal class and median class

• The modal class is the class with the highest frequency.
• The median class is the class containing the middle data point (find n/2 and see which class it falls in).

Diagrams to know

• Bar chart — bars don't touch, used for categorical data.
• Histogram — bars touch, used for continuous data, with frequency density on the y-axis when class widths differ.
• Pie chart — angles are proportional to frequency. Each frequency × (360 / total) gives the angle.
• Frequency polygon — plot frequencies at midpoints, join with straight lines.

The mistakes that cost the most marks