Standard deviation measures how far the values typically are from the mean. A small standard deviation means the data is clustered near the mean.
From summary statistics, variance = Σx²/n − (Σx/n)², and standard deviation = √variance. With n = 10, Σx = 166 and Σx² = 3408: mean = 16.6, variance = 340.8 − 275.56 = 65.24, so the standard deviation is 8.08 to 3 s.f.
Worked example
n = 6, Σx = 105 and Σx² = 2119. Find the variance.
- Mean = 105 ÷ 6 = 17.5.
- Variance = 2119/6 − 17.5² = 353.17 − 306.25.
Answer:46.9 (3 s.f.)
Key words
- variance
- the mean of the squared distances from the mean
- standard deviation
- the square root of the variance
- Σ
- sum of
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Common Core-referenced: HSS-ID.A.2