Median – Measure of Central Tendency

Median –

Median is defined as the middle value of the series when arranged either in ascending or descending order. It is denoted by ‘M’.

M = [(N+1)/2] th item.

M = Median

N = total number of observations

It is a value which divides the arranged series into two equal parts in such a way that the number of observations smaller than the median is equal to the number greater than it.

According to Connor, ‘The median is that value of the variable which divides the group into two equal parts, one part comprising all values greater and other values less than the median’.

The sum of deviations from the median will be minimum if we ignore the signs,

∑ X – M = Minimum

Types of Series

Individual Series

M = [(N+1)/2] th item.

M = Median

N = total number of observations

Example

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Discrete Series

M = [(N+1)/2] th item.

M = Median

N = total number of observations

Example

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Continuous Series

M = L + [{(N/2 – cf)/f} × i ]

L = lower limit of the median class

cf = cumulative frequency of the class preceding the median class

f = frequency of the median class

i = size of class interval of the median class

Example

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Cumulative Frequency Series –

M = L + [{(N/2 – cf)/f} × i ]

Example

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Merits of Median

1. Easy to understand.

2. Easy to locate.

3. Not affected by extreme values.

4. Can be located graphically with the help of ogives.

5. It is a positional value.

6. More suitable for qualitative data.

7. Most appreciate in case of open ended classes.

8. It is rigidly defined.

Demerits of Median

1. Not based on all observations.

2. It requires arranging of data in ascending or descending order.

3. Not capable of further algebraic operations.

4. Difficult to calculate when data is very small (less) or large (more).

5. Affected by sampling fluctuations.