Arithmetic Mean: It is a value obtained by adding together all the items and by dividing the total by the number of items. It is also called average. It is the most popular and widely used measure for representing the entire data by one value.
Arithmetic mean may be either:
1. Simple arithmetic mean, or
2. Weighted arithmetic mean.
Properties of Arithmetic Mean:
1. The sum of deviations of the items from the arithmetic mean is always zero i.e.
∑(X–X) =0.
2. The Sum of the squared deviations of the items from A.M. is minimum, which is less than the sum of the squared deviations of the items from any other values.
3. If each item in the series is replaced by the mean, then the sum of these substitutions will be equal to the sum of the individual items.
Merits of A.M.:
1. It is simple to understand and easy to calculate.
2. It is affected by the value of every item in the series.
3. It is rigidly defined.
4. It is capable of further algebraic treatment.
5. It is calculated value and not based on the position in the series.
Demerits of A.M.:
1. It is affected by extreme items i.e., very small and very large items.
2. It can hardly be located by inspection.
3. In some cases A.M. does not represent the actual item. For example, average patients admitted in a hospital is 10.7 per day.
4. A.M. is not suitable in extremely asymmetrical distributions.