Q.The output (in tonnes) of a small factory over 5 consecutive days is: 2, 4, 6, 8, 10. Calculate the Standard Deviation by the direct (actual mean) method.

Standard deviation is the square root of the average of the squared deviations from the mean. …

Step 1 — Arithmetic mean.

Step 2 — Deviations and squared deviations from the mean.

Step 3 — Standard Deviation. …

Cross-check using the alternative (raw-values) formula $\sigma^2 = \dfrac{\Sigma X^2}{N} - \bar{X}^2$: $\Sigma X^2 = 4+16+36+64+100 = 220$, so $\dfrac{220}{5} - 6^2 = …

Dividing by N−1 instead of N (the sample-variance convention, not used at this Intermediate level unless specifically instructed); forgetting to take the square ro …