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← 📊 Descriptive Statistics

Mean, median, mode

4 min

Three ways to describe the centre of your data. Mean is the average, median is the middle value, mode is the most frequent value.

Why it matters

The right centre prevents misleading summaries — average income, for instance, is distorted by a few very rich people.

Key ideas

  • Mean = sum ÷ n; uses every value
  • Median = middle value after sorting; robust to outliers
  • Mode = most frequent value; works for categories too
  • Symmetric data: mean ≈ median
  • Right-skewed data: mean > median
  • Report mean with SD, median with IQR

Real-life research example

Monthly household income in a village survey: most families earn 15–25k, a few earn 300k. The median describes a typical family; the mean is pulled upward.

When to use

  • Mean: roughly symmetric numeric data
  • Median: skewed data or outliers
  • Mode: categories or discrete counts

When NOT to use

  • Don't average codes of categories (e.g. 1 = Muslim, 2 = Hindu)
  • Don't report only the mean for clearly skewed data

Mini example

Data: 2, 3, 3, 4, 18
Mean = 30 ÷ 5 = 6, median = 3, mode = 3
The value 18 drags the mean away from the typical case.

Quick takeaway

If mean and median are close, the data are roughly symmetric. If they differ a lot, trust the median.

Try it yourself

Enter 6–10 values from your own work (or try 2, 3, 3, 4, 18). Which centre would you report, and why? Write your reasoning, then compare it.

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