Q2 of 25 Page 346

If the median of 60 observations, given below is 28.5, find the values of x and y.


For median:


Since, given that: Median = 28.5


We know, median class = 20-30


Median is given by



Where,


L = Lower class limit of median class = 20


N/2 = 60/2 = 30 [∵, given: total observation = 60]


cf = cumulative frequency of the class preceding median class = 5 + x


f = frequency of the median class = 20


h = class interval of the median class = 10


Substituting these values in the formula of median, we get



⇒ Median = 20 + (25 – x)/2


⇒ 28.5 = (40 + 25 – x)/2


⇒ 57 = 65 – x


⇒ x = 65 – 57 = 8


Recall, N = 45 + x + y = 60 [given]


And x = 8


⇒ 45 + 8 + y = 60


⇒ 53 + y = 60


⇒ y = 60 – 53


⇒ y = 7


Thus, x = 8 and y = 7.


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