MEDIAN - DEFINITION AND CALCULATION
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.
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