Q. 34.3( 7 Votes )
Find the mean, median and mode of the following data:
Answer :
To find mean, we will solve by direct method:
We have got
Σfi = 25 & Σfixi = 4171
∵ 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 = 25
⇒ N/2 = 25/2 = 12.5
The cumulative frequency just greater than (N/2 = ) 12.5 is 16, so the corresponding median class is 150 - 200 and accordingly we get Cf = 10(cumulative frequency before the median class).
Now, since median class is 150 - 200.
∴ l = 150, h = 50, f = 6, N/2 = 12.5 and Cf = 10
Median is given by,
⇒ 
= 150 + 20.83
= 170.83
And we know that,
Mode = 3(Median) – 2(Mean)
= 3(170.83) – 2(169)
= 512.49 – 338
= 174.49
Hence, mean is 169, median is 170.83 and mode is 174.49.
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