Find the mean, median and mode of the following data: [CBSE 2013]

Class	0 - 50	50 - 100	100 - 150	150 - 200	200 - 250	250 - 300	300 - 350
Frequency	2	3	5	6	5	3	1

To find mean, we will solve by direct method:

We have got

Σf_i = 25 & Σf_ix_i = 4171

∵ mean is given by

⇒

⇒

To find median,

Assume Σf_i = N = Sum of frequencies,

h = length of median class,

l = lower boundary of the median class,

f = frequency of median class

and C_f = 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 C_f = 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 C_f = 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.