Q. 195.0( 1 Vote )
Find the mean, median and mode of the following data:
For equal class intervals, we will solve by finding mid points of these classes using direct method.
We have got
Σfi = 50 and Σfixi = 1500
∵ mean is given by
Thus, mean is 30.
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.
We have got
So, N = 50
⇒ N/2 = 50/2 = 25
The cumulative frequency just greater than (N/2 = ) 25 is 39, so the corresponding median class is 30 - 40 and accordingly we get Cf = 24(cumulative frequency before the median class).
Now, since median class is 30 - 40.
∴ l = 30, h = 10, f = 15, N/2 = 25 and Cf = 24
Median is given by,
= 30 + 0.67
Thus, median is 30.67.
Since, we have got mean = 30 and median = 30.67
Applying the empirical formula,
Mode = 3(Median) – 2(Mean)
⇒ Mode = 3(30.67) – 2(30)
⇒ Mode = 92.01 – 60 = 32.01
∴ Mean = 30, Median = 30.67 and Mode = 32.01
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