How to Calculate Median? (With Formula, Examples, Merits and Demerits)

Median is the middle value in a distribution. It is a positional average. Median divides the data into equal halves, wherein 50 percent of the values lie below the median and 50 percent of the values lie above the median. Before determining the middle value, the observations have to be arranged in an ascending or descending order. Once the data is arranged in ascending or descending order, the middle most value is the median value. It is the size of (N+1)/2th item, where N is the number of items in the data.

1. Individual Observations:

Example 1:

Calculate the median of 10, 5, 11, 8, 22, 15, 18, 17, 13.

Solution:

Example 2:

Calculate the median of 9, 10, 5, 11, 8, 22, 15, 18, 17, 13.

Solution:

2. Discrete Series:

When the data is in the form of a frequency distribution, the median is calculated following the steps given below:

(i) Arrange the data in ascending order or descending order.

(ii) Calculate the cumulative frequencies.

(iii) Apply the formula for calculating the median. Median = Size of (N+1)/2^th item, where N is the total of frequencies.

(iv) In the cumulative frequency column, look for the cumulative frequency that is equal to (N + 1)/2 or cumulative frequency that is just higher than this.

(v) The corresponding value of the variable is the value of the median.

3. Continuous Series:

Merits of Median:

1. It is easy to compute.

2. It is easy to understand.

3. It can be computed accurately even in case of open end classes.

4. It is unaffected by extreme values.

5. It can be used when data is qualitative in nature and is ranked or arranged in order.

6. It can be calculated by mere observation.

Demerits of Median:

1. The data has to be arranged in an ascending or descending order.

2. It is not based on all the values.

3. It could be affected by errors in sampling.

4. It is not an appropriate measure when the data is small.