Q. 45.0( 3 Votes )
Find the mode, median and mean for the following data:
Answer :
To find mean, we will solve by direct method:
We have got
Σfi = 100 & Σfixi = 4970
∵ 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 = 100
⇒ N/2 = 100/2 = 50
The cumulative frequency just greater than (N/2 = ) 50 is 71, so the corresponding median class is 45 - 55 and accordingly we get Cf = 38(cumulative frequency before the median class).
Now, since median class is 45 - 55.
∴ l = 45, h = 10, f = 33, N/2 = 50 and Cf = 38
Median is given by,
⇒ 
= 45 + 3.64
= 48.64
And we know that,
Mode = 3(Median) – 2(Mean)
= 3(48.64) – 2(49.7)
= 145.92 – 99.4
= 46.52
Hence, mean is 49.7, median is 48.64 and mode is 46.52.
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