# Find the mean, mode and median of the following frequency distribution:

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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