• Discrete vs continuous data — discrete data is counted (whole steps), continuous data is measured (any value on a scale).
• Mode, median, mean — three different ways to describe "the typical value," each with strengths and weaknesses.
• Calculations with the mean — rearranging mean = total ÷ number of values to solve backwards problems.
• Averages from frequency tables — finding mode, median, and mean when data is summarised in a table rather than listed out.
• Averages from grouped data — when exact values are hidden in groups, you can only estimate the mean using midpoints, and you find the modal class / median class instead of exact values.
• Calculators — using one-variable statistics mode to get mean, median, and quartiles instantly (for both raw and grouped data).
• Range & Interquartile Range (IQR) — two measures of spread; IQR is more resistant to extreme values.
• Comparing data sets — always compare an average AND a spread, and explain what each comparison means in real-world terms.

What's the difference?

Numerical data splits into two families, and knowing which one you're dealing with matters for how you group and analyse it later.

• Continuous data can take any value on a scale — there are no "gaps" between possible values. Think height, weight, length, time, temperature. If you zoom in with a more precise instrument, you always find more decimal places are possible.
• Discrete data can only take particular, separate values — there are gaps. Usually this means counting something (number of pets, number of cars) so it's whole numbers, but it doesn't have to be — shoe sizes include "halves" (6, 6.5, 7) yet are still discrete because you can never get a shoe size of 6.3.

Three ways to find "the average"

In everyday speech we say "the average," but in maths there are three distinct averages, and picking the wrong one for a data set can genuinely mislead people. Think of them like three different photographers trying to capture "what this data looks like" — each one focuses on a different feature.

• Mode — the value that appears most often. It's the only average you can use on non-numerical (categorical) data like favourite colours or pet types. A data set can have no mode, one mode, or several modes (this is called bimodal if there are two).
• Median — the middle value once the data is sorted into order. If there's an even number of values, it's the midpoint (average) of the two middle numbers.
• Mean — the sum of all values divided by how many values there are. This is the "share it out equally" average — it uses every single data point, which makes it powerful but also vulnerable to being dragged by extreme values.

Which average should I use?

This is a genuinely important exam skill, not just theory. Here's the decision logic: