The table below shows the daily expenditure on food of 30 households in a locality:

Daily expenditure (in Rs.)	Number of households
100 - 150	6
150 - 200	7
200 - 250	12
250 - 300	3
300 - 350	2

Find the mean and median daily expenditure on food. [CBSE 2009C]

To find mean, we will solve by direct method:

We have got

Σf_i = 30 & Σf_ix_i = 6150

∵ 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 = 30

⇒ N/2 = 30/2 = 15

The cumulative frequency just greater than (N/2 = ) 15 is 25, so the corresponding median class is 200 - 250 and accordingly we get C_f = 13(cumulative frequency before the median class).

Now, since median class is 200 - 250.

∴ l = 200, h = 50, f = 12, N/2 = 15 and C_f = 13

Median is given by,

⇒

= 200 + 8.33

= 208.33

Hence, mean is 205 and median is 208.33