Properties of Median in Statistics

The median of a given set of data values refers to the middlemost observation in the given data set. It is the value that divides our data into exactly two equal parts. In this article, we list some of the main properties of the median in statistics.

Properties of Median in Statistics:

1. When the data is arranged in either ascending or descending order then the median divides the data in such a way that exactly 50% of the data lies below it and 50% of the data lies above it.
2. The median is a positional average. This means that it is calculated on the basis of its position when the data values are arranged in order.
3. The median can not only be determined for ratio and interval scale, but it can also be calculated for ordinal type of data where the data values can be arranged in order of rank. An example of such type of data is singing ability which cannot be measured numerically. but we can definitely rank 10 people according to their singing ability from highest to lowest and hence find the median.
4. The median is not affected by the presence of extreme values or outliers. This is because the median is calculated only on the basis of the middlemost observations. Since the extreme values play no role in its calculation, it remains unaffected by them.
5. Change of Scale: If every data values gets multiplied by a particular number then the median is also multiplied by the same number. For example, the median of the numbers 1, 2, 3, 4, and 5 is the middle value, that is, 3. If all values are multiplied by two then the data set is 2, 4, 6, 8, 10. We notice that the value of the median for the new data set is 6 which is indeed equal to 2 times the old median. This property is known as the change of scale property.
6. Change of Origin: If we add a fixed number to all of the data values then the same fixed number gets added to the median. For example, we know that the median of the numbers 1, 2, 3, 4, and 5 is 3. If we add 2 to each data value then the new data set is 3, 4, 5, 6, and 7. Thus we see that the new median is equal to 5 which is indeed 2 more than the old median.
7. The median is much more simple to understand for the layman or the common man compared to other statistical measures such as variance, correlation, etc. since no complicated calculations are required to calculate it.
8. If the number of data values is small then the median can be calculated simply by inspection and finding out the middlemost value.
9. The median is affected much more by fluctuations in sampling. this means that the median of a sample cannot be used as a good estimate for the median of the entire population.
10. We cannot combine the median of two different data sets to obtain the median of the combined data set. This means that the median is not capable of algebraic treatment.
11. The median can be calculated in a graphical manner by drawing a cumulative frequency curve/ogive.