Q. 14.7( 7 Votes )
Find the mean, mode and median of the following frequency distribution:
Answer :
To find mean, we will solve by direct method:
We have got
Σfi = 50 & Σfixi = 1910
∵ mean is given by
⇒ 
⇒ 
To find median,
Assume Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table.
So, N = 50
⇒ N/2 = 50/2 = 25
The cumulative frequency just greater than (N/2 = ) 25 is 37, so the corresponding median class is 40 - 50 and accordingly we get Cf = 25(cumulative frequency before the median class).
Now, since median class is 40 - 50.
∴ l = 40, h = 10, f = 16, N/2 = 25 and Cf = 25
Median is given by,
⇒ 
= 40 + 0
= 40
And we know that,
Mode = 3(Median) – 2(Mean)
= 3(40) – 2(38.2)
= 120 – 76.4
= 43.6
Hence, mean is 38.2, median is 40 and mode is 43.6.
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