Guide · Updated November 2026 · How we check our numbers

Mean, Median, Mode and Standard Deviation Explained

Averages describe the center of a data set; standard deviation describes how spread out it is.

Mean, median and mode

For the scores 88, 92, 75, 92, 81, 67:

• Mean (sum ÷ count) = 495 ÷ 6 = 82.5
• Median (middle value after sorting 67, 75, 81, 88, 92, 92) = (81 + 88) ÷ 2 = 84.5
• Mode (most frequent) = 92

The median is better than the mean when a few extreme values would pull the average up or down, such as house prices or incomes.

Standard deviation step by step

For 2, 4, 4, 4, 5, 5, 7, 9: the mean is 5. Subtract the mean from each value and square it: 9, 1, 1, 1, 0, 0, 4, 16. The sum is 32.

• Population variance = 32 ÷ 8 = 4, so σ = 2
• Sample variance = 32 ÷ 7 ≈ 4.571, so s ≈ 2.138

Sample or population?

Use the population formula when you have every value in the group; use the sample formula when your data is a selection from a bigger group.

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This guide is general information, not professional advice.