Mean, Median & Mode Calculator

The three averages — mean, median and mode — each summarise a data set differently. The mean is the sum divided by the count, affected by outliers. The median is the middle value when sorted, resistant to outliers. The mode is the most frequent value, useful for categorical data.

This calculator finds all three averages plus the range (highest minus lowest). It sorts your data, highlights the median position and identifies all modes (a set can have multiple modes or no mode at all). Results include step-by-step working for each measure.

Mean, median, mode — three averages. MEAN: sum ÷ count (arithmetic average). MEDIAN: middle value when sorted. MODE: most frequent value. Sample data [2, 4, 4, 5, 8]: mean = 23/5 = 4.6; median = 4 (middle); mode = 4 (most frequent). Each tells different story. Mean uses ALL data points but distorted by outliers. Median ignores outliers (robust). Mode shows typical category (categorical or discrete data).

When to use each — UK statistics. UK household income: median (£35,000) vs mean (£40,000) — mean inflated by high earners. Property prices: median better than mean for 'typical' market. Exam scores: mean usually appropriate (assumes normal distribution). Survey responses on Likert scale (1-5): mode shows most-common opinion. Test data with outliers (sales, salaries): median + interquartile range better than mean + standard deviation. UK government statistics generally favour MEDIAN for incomes and property values.

Real UK examples. UK median household income 2024: £35,000 (ONS). Mean: £40,000. Median UK house price 2026: £290,000 (HMLR). Mean: £370,000 (skewed by London £1M+). Median UK weekly earnings full-time: £692 (April 2024). Median full-time UK gross hourly pay: £17.43. Mean rent (private sector): £1,200/month UK; £1,750 London. Knowing whether 'average' means mean or median matters — official statistics usually median for skewed distributions.

How outliers affect each average. Sample salaries [25k, 28k, 30k, 35k, 40k, 250k]: mean = 68k (misleading high — distorted by 250k); median = 32.5k (accurate 'middle'). Mode: no mode (all unique). Skew matters: positive skew (long right tail — incomes, property, sales) — median < mean. Negative skew (top-heavy, ceiling effects — exam scores capped at 100%): median > mean. Symmetric (heights, weights): mean ≈ median ≈ mode. Real-world data rarely symmetric.

UK statistics terms in news. 'Average UK salary': always check mean vs median. 'Median worker' references: 50th percentile — half earn more, half less. 'Average household pays £X council tax': usually mean — pulled up by expensive boroughs. 'Average wait time NHS': often quoted as median because outliers distort. Standard deviation: tells you spread. Reliable stats source: ONS (gov.uk/ons) — uses median and interquartile range for most income/wealth statistics. Beware tabloid 'average' figures — often most-favourable measure chosen.