Standard Deviation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

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Find the population standard deviation of

\{6, 2, 3, 1\}

1
Mean: $\bar{x} = \frac{6+2+3+1}{4} = 3$ . Squared deviations: $9, 1, 0, 4$ . Sum $= 14$ .
2
Variance: $\sigma^2 = \frac{14}{4} = 3.5$ . Standard deviation: $\sigma = \sqrt{3.5} \approx 1.87$ .

Answer

\sigma \approx 1.87

Follow the standard deviation formula step by step: find the mean, compute squared deviations, average them, and take the square root.

About Standard Deviation

The standard deviation measures the average distance of data values from the mean, giving a typical spread around the center.

Find the population standard deviation of [formula].

Find the sample standard deviation of [formula].

Compare the population standard deviations of [formula] and [formula].