Statistics & Data
Calculators, worked examples and guides — from mean, median and mode through to probability, scatter diagrams and cumulative frequency.
Learning about Statistics & Data
The key idea: statistics is about making sense of data — collecting it, summarising it, and drawing conclusions from it. The three averages (mean, median, mode) each describe "typical" in a different way. None is universally best.
Type 1 — Mean
"Find the mean of 4, 7, 9, 12, 8"
Step 1: Add all values: 4 + 7 + 9 + 12 + 8 = 40.
Step 2: Divide by count: 40 ÷ 5 = 8
Shortcut: Sum ÷ Count — write both in your working
Type 2 — Median
"Find the median of 3, 7, 2, 9, 5"
Step 1: Sort in order: 2, 3, 5, 7, 9.
Step 2: Find the middle position: (5+1)÷2 = 3rd value.
Step 3: Median = 5
Shortcut: For n values, median is at position (n+1)÷2. For even n, average the two middle values.
Type 3 — Probability
"A bag has 3 red and 5 blue balls. What is P(red)?"
Step 1: Total balls = 3 + 5 = 8.
Step 2: Favourable outcomes = 3.
Step 3: P(red) = 3/8 = 0.375 = 37.5%
Shortcut: P(event) = favourable outcomes ÷ total outcomes — always between 0 and 1
Statistics & Probability Formula Sheet & Rules
Need a printable revision sheet? Access rules for central tendency (mean, median, mode), spread and dispersion (IQR, standard deviation, Tukey outlier fences), and probability laws with step-by-step worked examples and custom print export.
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Statistics Questions Answered
What is the mean?
The mean is the sum of all values divided by the count of values. It gives the arithmetic average. A single extreme value (outlier) can pull the mean away from the centre of the data.
What is the median?
The median is the middle value when data is sorted in order. For an even number of values, it is the mean of the two middle values. The median is not affected by outliers, making it useful for skewed data.
What is the mode?
The mode is the most frequently occurring value. A data set can have more than one mode (bimodal or multimodal), or no mode if all values appear the same number of times.
What is probability?
Probability measures how likely an event is to occur, on a scale from 0 (impossible) to 1 (certain). P(event) = number of favourable outcomes ÷ total possible outcomes.
What is the range?
The range is the difference between the highest and lowest values in a data set. It measures the spread of the data. A large range indicates the data is widely spread; a small range indicates it is clustered closely.