Mathematics

The table below shows the daily expenditure on food of 25 households in a locality.
Daily expenditure (in ₹) Number of households
100 - 150 4
150 - 200 5
200 - 250 12
250 - 300 2
300 - 350 2
Find the mean daily expenditure on food by a suitable method.

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We will use step deviation method to find the mean.

In the following table a is the assumed mean and h is the class size.

Here, h = 50.

By formula,

Class mark = $\dfrac{\text{Upper limit + Lower limit}}{2}$

Daily expenditure (in ₹)	Number of households (f_i)	Class mark (x_i)	d_i = x_i - a	u_i = (x_i - a)/h	f_iu_i
100 - 150	4	125	-100	-2	-8
150 - 200	5	175	-50	-1	-5
200 - 250	12	a = 225	0	0	0
250 - 300	2	275	50	1	2
300 - 350	2	325	100	2	4
Total	Σf_i = 25				Σf_iu_i = -7

By formula,

Mean = a + $\dfrac{Σf$

Substituting values we get :

$\text{Mean } = 225 + \dfrac{-7}{25} \times 50 \\[1em] = 225 + (-14) \\[1em] = 211$

Hence, mean daily expenditure on food = ₹ 211.

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