Question

The median class of a frequency distribution is 125-145. The frequency of the median class and cumulative frequency of the class preceding to the median class are 20 and 22 respectively. Find the sum of frequencies if the median is 137

Answer 1

the sum of frequencies  = 68 for The median class of a frequency distribution is 125-145 & 137 Median

Step-by-step explanation:

This formula is used to find the median in a group data which is located in the median class.

Median, m = L + [ (N/2 – F) / f ]C

L  lower boundary of the median class  = 125

N  sum of frequencies  = ?

F  cumulative frequency before the median class = 22

f - frequency of median group = 20

C - Class Size = 20

137 = 125 + [( N/2 - 22) / 20 ] 20

=> 137  = 125 +  (N - 44)/2

=> 12 = (N - 44)/2

=> N - 44 = 24

=> N = 68

the sum of frequencies  = 68

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Answer 2

The sum of frequencies is 68 .

Explanation:

Formula : Median = $l+\dfrac{\dfrac{n}{2}-cf}{f}(h)$

, where l= Lower limit of median class

n = Sum of frequency

cf = cumulative frequency of the class preceding to the median class

f= frequency of the median class

h= Class width

Given : The median class of a frequency distribution is 125-145.

Then , l= 125

h= 145-125=20

f=20

cf=22

Median = 137

Put all theses values in formula , we get

$137=125+\dfrac{\dfrac{n}{2}-22}{20}(20)$

$137-125=\dfrac{n}{2}-22$

$12=\dfrac{n}{2}-22$

$12+22=\dfrac{n}{2}$

$34=\dfrac{n}{2}$

$n=2(34)=68$

∴  The sum of frequencies is 68 .

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