Question

The table below shows the daily expenditure on the food of 25 households in a locality.

Daily expenditure (in Rs.)	100-150	150-200	200-250	250-300	300-350
Number of households	4	5	12	2	2

Find the mean daily expenditure on food by a suitable method.

Answer 1

Hint: Here we are given the daily expense and number of households falling in that range. To find mean we will directly use a formula to find mean. But we also have to find the middle value of the daily expense range. This middle value acts as a representative of the other frequencies falling in that class.

Complete step-by-step answer:
Now we will use the direct method for calculation. Let’s tabulate the data.
The middle value or class mark of a frequency range is given by,
Mid-value $ = \dfrac{{upper\,limit + lower\,limit}}{2}$
The frequency table is,

Daily Expense	No. of households (${f_i}$)	Mid value (${x_i}$)	${f_i}{x_i}$
100-150	4	125	500
150-200	5	175	875
200-250	12	225	2700
250-300	2	275	550
300-350	2	325	650
Total	$\sum {{f_i}} = 25$		$\sum {{f_i}{x_i}} = 5275$

We know that the general formula to find the mean value is,
Mean $ = \dfrac{{\sum {{x_i}{f_i}} }}{{\sum {{x_i}} }}$
Now, we will substitute the value for the sum of the product of frequency and midpoint and the value for the sum of total frequency.
$ \Rightarrow $ Mean $ = \dfrac{{5275}}{{25}}$
Divide numerator by the denominator,
$\therefore $ Mean $ = 211$

Hence the daily expense of food is 211.

Note: Here in this problem data given of classes are in grouped form. No direct numbers are given so do find the middle values or class mark of the range. And then proceed for calculations. Always tabulate these types of problems.
In the mean formula, while computing $\sum {fx} $, don’t take the sum of $f$ and $x$ separately and then multiply them. It will be difficult. Students should carefully make the frequency distribution table; there are high chances of making mistakes while copying and computing data.