Q.The sales (₹ lakh) of a company over 5 years are: 10, 20, 30, 40, 60. Using an assumed mean of 30, calculate the Standard Deviation by the short-cut (assumed mean) method, and verify your answer using the direct (actual mean) method.

The short-cut method computes Standard Deviation using deviations from any convenient assumed value, not necessarily the actual mean. …

Step 1 — Deviations from the assumed mean, A = 30.

Step 2 — Squares of the deviations.

Step 3 — Apply the short-cut formula ($N=5$): …

Cross-check via the direct (actual mean) method. Actual mean $\bar{X} = \frac{10+20+30+40+60}{5} = \frac{160}{5} = 32$. Deviations from 32: $-22,-12,-2,8,28$; squares: $484,144,4,64,784$; sum $= 1480$; variance $= 1480/5 = 296$ — exactly matching the v …

Forgetting to SUBTRACT the correction term $(\Sigma d/N)^2$ when the assumed mean differs from the actual mean — omitting it (i.e., just usi …