Question

Table shows the daily expenditure on food of 25 households in a locality.

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

Find mean daily expense on food by suitable method.

Answer 1

Hint: Here we are given with the daily expense and number of households falling in that range. To find mean we will directly use 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.
Formula used:
Mean \[ = \dfrac{{\sum {{f_i}{x_i}} }}{{\sum {fi} }}\]

Complete step-by-step answer:
Now we will use the direct method for calculation. Let’s tabulate the data.
Middle value or class mark of a frequency range is given by
 \[middle = \dfrac{{upper\lim it + lower\lim it}}{2}\]

Daily expense	Number of households\[fi\]	Class mark/middle value \[{x_i}\]	\[{f_i}{x_i}\]
100-150	4	\[\dfrac{{150 + 100}}{2} = 125\]	\[4 \times 125 = 500\]
150-200	5	\[\dfrac{{200 + 150}}{2} = 175\]	\[5 \times 175 = 875\]
200-250	12	\[\dfrac{{250 + 200}}{2} = 225\]	\[12 \times 225 = 2700\]
250-300	2	\[\dfrac{{300 + 250}}{2} = 275\]	\[2 \times 275 = 550\]
300-350	2	\[\dfrac{{350 + 300}}{2} = 325\]	\[2 \times 325 = 650\]

 Now let’s get the sums.
\[{f_i} = 4 + 5 + 12 + 2 + 2 = 25\]
\[{f_i}{x_i} = 500 + 875 + 2700 + 550 + 650 = 5275\]
Putting these values in formula,
Mean \[ = \dfrac{{\sum {{f_i}{x_i}} }}{{\sum {fi} }}\]
\[
   \Rightarrow \dfrac{{5275}}{{25}} \\
   \Rightarrow 211 \\
\]
Thus daily expense on food is Rs.211.
Note: Here in this problem data given of classes is 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. Be attentive while calculating because the whole problem involves calculations nothing else.