Spread & Deviation
Grades 9–11 Statistics Data
Two classes can share a 75% average while one is tight (72–78) and the other wild (40–100). The mean can't see the difference — spread can.
Standard deviation — typical distance from the mean
- Find the mean.
- Subtract it from every value (deviations).
- Square the deviations, average the squares (variance).
- Square-root back down — the standard deviation.
Data 2, 4, 4, 6, 9 mean = 5
Deviations: −3, −1, −1, +1, +4
Squares: 9, 1, 1, 1, 16 sum = 28
Variance: 28 ÷ 5 = 5.6
Std dev: √5.6 ≈ 2.37
→ a "typical" value sits ~2.4 from the mean
Why square?
Deviations would cancel to zero — positives and negatives wipe
out. Squaring makes distance always positive and punishes big
outliers harder. The square root then restores original units.
Practice
Data 2, 4, 6, 8 — mean = ___
Squared deviations are 9, 4, 1, 0, 15 — their sum = ___
Variance 9 → standard deviation = ___
Class A scores 70–80; class B scores 30–100, same mean. Which has the larger standard deviation?
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