Median

The median by definition refers to the middle value in a distribution. In case of median one-half of the items in the distribution have a value the size of the median value or smaller and one-half have a value the size of the median value or larger. The median is just the 50th percentile value below which 50% of the values in the sample fall. It splits the observations into two halves.
As distinct from the arithmetic mean which is calculated from the value of every item in the series, the median is what is called a positional average. The term ‘position’ refers to the place of a value in a series. The place of the median in a series is such that an equal number of items lie on either side of it.

Merits and Limitations of Median

Merits:

1.    It is especially useful in case of open-end classes since only the position and not the values of items must be known. The median is also recommended if this distribution has unequal classes, since it is easier to compute than the mean.

2.    It is not influenced by the magnitude of extreme deviations from it.

3.    In markedly skewed distributions such as income distributions or price distributions where the arithmetic mean would be distorted by extreme values the median is especially useful. Consequently, the median income for some purposes be regarded as a more representative figure, for half the income earners must be receiving at least the median income. One can say as many receive the median income as do not.

4.    It is the most appropriate average in dealing with qualities data, i.e., where ranks are given or there are other types of items that are not counted or measured but are scored.

5.    The value of median can determined graphically whereas the value of mean cannot be graphically ascertained.

6.    Perhaps the greatest advantages of median is, however, the fact that the median actually does indicate what many people incorrectly believe arithmetic mean indicates. The Median indicates the value of the middle item in the distribution. This is a clear-cut-meaning and makes the median a measure that can be easily explained.

Limitations:

1.    For calculating median it is necessary to arrange the data; other averages do not need any arrangement.

2.    Since it is a positional average, its value is not determined by each and every observation.
3.    It is not capable of algebraic treatment.

4.    The value of median is affected more by sampling fluctuations than the value of arithmetic mean.

5.    The median, in some cases, cannot be computed exactly as can the mean. When the number of items included in a series of data is even, the median is determined approximately as the mid-point of the two middle items.

6.    It is erratic if the number of items is small.

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