Median

The median is a variate value which divides the given data into two equal parts. If the data are arranged either in ascending or descending order, the middlemost number is median.
For example,
1, 3, 8, \(\underline{10}\), 13, 16, 20
The middle number 10 is median.

Calculation of median for individual series

The formula for calculating median for individual series is given by;
Median (Md) = Position of \((\frac{N + 1}{2})\)^th item
where, N = No. of observation or items.

The steps for calculation of median for individual series:

1. Arrange the data in ascending or descending order.
2. Count the number of terms (n).

Calculation of median for a discrete data

Let, x₁, x₂, x_{3..................}x_n be the variable values and f₁, f₂, f₃,............ f_n be their corresponding frequency respectively.
Then, Median (Md) = Position of \((\frac{N + 1}{2})\)^th item
where, N = total sum of a frequency

Calculation of median for a continuous data

To calculate the median for a continuous data, the following steps are applied:

1. Prepare cumulative frequency table
2. Find the value of \((\frac{N}{2})\)^th items which gives the median class.
3. Use the formula, Median = l + \(\frac{\frac{N}{2}− c.f}{f}\) × i
   where,
   l = lower limit of median class
   c.f = cumulative frequency
   f = frequency
   i = class interval