Q.Find the A.M. for the data 30, 20, 32, 16, 27.

The arithmetic mean is the sum of all observations divided by their number. For an individual series it is computed directly as $\bar X=\Sigma X/N$, or by the short-cut (assumed mean) method $\bar X = A + \Sigma d/N$ using deviations $d=X-A$. For a discrete series the same two methods apply weighted by frequency: $\bar X=\Sigma fX/N$ or $\bar X=A+\Sigma fd/N$. For a continuous series, the step-deviation method is generally quickest: $\bar X = A + (\Sigma fd'/N)\times h$, with $d'=(m-A)/h$ computed from each class's …