Mean, median and mode all three are Central Tendency or Averages. The Arithmetic mean lies under Mathematical Average and the other two Median and Mode are types of Positional Averages.
A measure of central tendency is a typical value around which the figures congregate”. The value of central tendency or average always lies between the minimum and maximum values.
- Median is an average which divides a distribution into 2 equal halves.
- When we arrange values in ascending order, the middle value is the median.
- Median is represented by the letter ‘Md”.
- Median can also be calculated by:
- Ungrouped data
- Discrete series
- Continuous series
1.Individual series or Ungrouped data
Step 1- Arrange the data in ascending or descending order.
Step 2- Apply the formula
Md = Median
N = total number of items= Sf
2. Discrete series
Step 1- Arrange the data in ascending or descending order
Step2- Find the cumulative frequencies
Step 3- Apply formula
Md = Median
N = total number of Items
3. Continuous series :
Step 1- Find the cumulative frequencies
Step2- Find out the median class by using
Step 3- Apply the formula
L = lower limit of the median class
cf = cumulative frequency prior to the median class
f = actual frequency of the median class
c = class interval of the median class.
MERITS OF THE MEDIAN
- It is simple to calculate and easy to understand.
- It can be located by inspection . So it is an inspectional value
- The value of median is unaffected by extreme values
- Its value generally lies in the distribution
- It is further used in statistical calculations
DEMERITS OF THE MEDIAN
- Median is not a familiar average like mean.
- In the large ungrouped data, the calculation of median is tedious because of the rearranging data into ascending or descending order.
- Since it is positional average , its value is not influenced by each and every observations.
- The median value is affected by sampling fluctuations.