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Which is the correct formula for median of grouped data? Consider: L= lower limit of median class CF_0= cumulative frequency of preceding cla
Question

Which is the correct formula for median of grouped data?
Consider:
L= lower limit of median class
CF_0= cumulative frequency of preceding class
F= frequency of median class
H= class width
N= the total of frequency

A.

(N/2CF0)F×H\frac{( N/2-CF_0)}F×H​​

B.

L+(N/2CF0)F×HL+\frac{(N/2-CF_0)}F×H​​

C.

L+(N/2CF0)FL+\frac{(N/2-CF_0)}F​​

D.

L+N2CF0F×HL+\frac N2-CF_0-F×H​​

Correct option is B

Solution:

Median=L+(N/2CF0F)×H\text{Median} = L + \left( \frac{N/2 - CF_0}{F} \right) \times H 

Where: 

L = Lower limit of the median class

CF0CF_0 = Cumulative frequency of the class preceding the median class

F = Frequency of the median class

H = Class width (difference between the upper and lower limit of the median class)

N = Total frequency (sum of all frequencies) 

Thus, Option(b) is correct.


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