Find the mean, median and mode of the following data: [CBSE 2008]

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120	120 - 140
Frequency	6	8	10	12	6	5	3

To find mean, we will solve by direct method:

We have got

Σf_i = 50 & Σf_ix_i = 3120

∵ 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 = 50

⇒ N/2 = 50/2 = 25

The cumulative frequency just greater than (N/2 = ) 25 is 36, so the corresponding median class is 60 - 80 and accordingly we get C_f = 24(cumulative frequency before the median class).

Now, since median class is 60 - 80.

∴ l = 60, h = 20, f = 12, N/2 = 25 and C_f = 24

Median is given by,

⇒

= 60 + 1.67

= 61.67

And we know that,

Mode = 3(Median) – 2(Mean)

= 3(61.67) – 2(62.4)

= 185.01 – 124.8

= 60.21

Hence, mean is 62.4, median is 61.67 and mode is 60.21.