Question

Write answers for the following questions

Define arithmetic mean-state the merits and demerits of the mean.

Answer 1

The arithmetic mean refers to the value calculated by dividing the sum of the values of the given items by the total number of items in a series. Mathematically,

$\overline{X}=\frac{x_1+x_2+x_3+......+x_n}{N}$
Merits:

i. Simple to calculate: The arithmetic mean is simple and easy to calculate, as it is measured using a simple formula.
ii. Rigidly defined: It implies that the resultant value remains the same, irrespective of the method used for calculation.
iii. Sample fluctuations: The mean is stable in nature; it is not much affected by fluctuations in sampling.

Demerits:

i. Absurd results: It is often seen that the mean gives absurd or unreliable results, which are unrealistic in nature.
ii. Inaccurate in some cases: The mean is not suitable in case the data given is incomplete. This is because if even a single item or value is missing, the mean loses its accuracy.
iii. Affected by extreme values: The mean gets affected by extreme values, as this measure is based on all the items of the given data.