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Results on Median ( M )

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☼ Results on Median ( M ) :

(i) Ungrouped Data : –

First of all arrange the data in ascending or descending order of magnitude, then

M = $\left (\frac{n+1}{2} \right )^{th}$ Observation.

(ii) Discrete Data ( Grouped Data ) : –

First of all arrange the data in ascending or descending order of magnitude, then

M = $\left (\frac{n+1}{2} \right )^{th}$ Observation. ; n = $\sum f_{i}$ .

(iii) Continuous Data ( Grouped Data ) : –

First arrange all the Classes of Frequency Distribution in ascending order and also find the cumulative frequencies, then

Median Class = The class in which $\left (\frac{n}{2} \right )^{th}$ observation lies ; n = $\sum f_{i}$ .

Note : This can be found out from cumulative frequencies.

Now, M = L + $\frac{\frac{n}{2}-cf}{f}\times C$

Where, L = Lower limit of Median Class

= $\sum f$ = Sum of frequencies

cf = Cumulative frequency of the class preceding the median class.

f = Frequency of Median Class

C = Class-Length of Median Class