Q. 24.4( 26 Votes )

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Answer :

Using points (38,0), (40,3), (42,5), (44,9), (46,14), (48,28), (50, 32) and (52,35), plot a graph.


To find median graphically,


We have total frequency, N = 35


N/2 = 35/2 = 17.5


Plot 17.5 on the y-axis and draw a horizontal line intersecting the ogive parallel to x-axis.



Observe, from the graph the vertical line parallel to y-axis touches y-axis at 46.5 (approx.).


Hence, median is 46.5.


Finding median by formula:



For median:


We have, total frequency, N = 35


N/2 = 35/2 = 17.5


Observe, cf = 28 is just greater than 17.5.


Thus, median class = 46-48


Median is given by



Where,


L = Lower class limit of median class = 46


N/2 = 17.5


cf = cumulative frequency of the class preceding median class = 14


f = frequency of the median class = 14


h = class interval of the median class = 2


Substituting these values in the formula of median, we get




Median = 46 + 0.5


Median = 46.5


Thus, median is 46.5.


Hence, verified.


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