The following table gives the daily income of 50 workers of a factory:

Daily income (in Rs.)	100 - 120	120 - 140	140 - 160	160 - 180	180 - 200
Number of workers	12	14	8	6	10

Find the mean, mode and median of the above data. [CBSE 2009]

To find mean, we will solve by direct method:

We have got

Σf_i = 50 & Σf_ix_i = 7260

∵ 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 26, so the corresponding median class is 120 - 140 and accordingly we get C_f = 12(cumulative frequency before the median class).

Now, since median class is 120 - 140.

∴ l = 120, h = 20, f = 14, N/2 = 25 and C_f = 12

Median is given by,

⇒

= 120 + 18.57

= 138.57

And we know that,

Mode = 3(Median) – 2(Mean)

= 3(138.57) – 2(145.2)

= 415.71 – 290.4

= 125.31

Hence, mean is 145.2, median is 138.57 and mode is 125.31.