### Question: What do you mean by Arithmetic Mean? Differentiate between Simple and Weighted Arithmetic Mean. When is the usage of median is considered more appropriate than mean?

ARITHMETIC MEAN: Arithmetic Mean or the mean is the number which is obtained by dividing the values of all the items of the series and dividing the total by number of items.

Arithmetic Mean is denoted by x̄. It can be represented by the following formula:

Mean= x̄ =

OR

Mean= Sum of value of items/ Total number of items.

Arithmetic Mean can be of two types:

Simple Arithmetic Mean: In simple arithmetic mean, all items of a series are given equal importance.

Weighted Arithmetic Mean: Under Weighted Arithmetic Mean, different items of the series are assignment weights according to their relative importance.

#### CASES WHEN USAGE OF MEDIAN IS CONSIDERED APPROPRIATE THAN MEAN

Median is a positional measure. It is the middle value of the series.  It is the value that divides the series into two equal parts. Thus, the values less than and more than median will be equal. It is denoted by M.

Median should be preferred over Mean in the following cases:

1. In case of data containing the extreme values, median should be applied rather than the mean. It is so because median is not affected by the value of extreme items in the series and mean get affected a lot by the extreme items. This happens because in case of mean we take the value of item but in median we only consider the number of items not the values of the item.

2. Median should be used where the distribution of data values is skewed.

3. Median should be used where the data is to presented using the graph. This is so because median can be calculated by using Less than ogives and More than ogives graph but arithmetic mean cannot be calculated by using the graphic method.

4. Median is preferred over mean to those areas where direct quantitative measurement is not possible. It is not possible to measure intelligence directly. But it is possible to arrange the group of persons in ascending or descending order of intelligence to locate who is the most intelligent person.

5. In case of open end series, median is preferred over mean. There is no need in median to convert the open end series into close end series but in case of mean, the open end series need conversion.