Question

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

Answer 1

Question:

The table given below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by assumed mean method.

$\displaystyle\begin{array}{|c|c|}\cline{1-2}\bf\:Daily\:expenditure\:(\:in\:rupees\:) & \bf\:No.\:of\:households\\\cline{1-2}\sf\:100\:-\:150 & \sf\:4\\\cline{1-2}\sf\:150\:-\:200 & \sf\:5\\\cline{1-2}\sf\:200\:-\:250 & \sf\:12\\\cline{1-2}\sf\:250\:-\:300 & \sf\:2\\\cline{1-2}\sf\:300\:-\:350 & \sf\:2\\\cline{1-2}\end{array}$

Answer:

The mean daily expenditure on food is Rs. 211.

Step-by-step-explanation:

We have given the distribution of expenditure on food by 25 households.

We have to find the mean daily expenditure on food using assumed mean method.

$\displaystyle\begin{array}{|c|c|c|c|c|}\cline{1-5}\bf\:Class & \bf\:Class\:marks\:(\:x_i\:) & \bf\:d_i\:=\:x_i\:-\:A & \bf\:Frequency\:(\:f_i\:) & \bf\:f_i\:\times\:d_i\\\cline{1-5}\sf\:100\:-\:150 & \sf\:125 & \sf\:-\:100 & \sf\:4 & \sf\:-\:400\\\cline{1-5}\sf\:150\:-\:200 & \sf\:175 & \sf\:-\:50 & \sf\:5 & \sf\:-\:250\\\cline{1-5}\sf\:200\:-\:250 & \sf\:225\:\rightarrow\:A & \sf\:0 & \sf\:12 & \sf\:0\\\cline{1-5}\sf\:250\:-\:300 & \sf\:275 & \sf\:50 & \sf\:2 & \sf\:100\\\cline{1-5}\sf\:300\:-\:350 & \sf\:225 & \sf\:100 & \sf\:2 & \sf\:200\\\cline{1-5}\sf\:Total & & & \sf\:\sum\:f_i\:=\:25 & \sf\:\sum\:f_i\:d_i\:=\:-\:350\\\cline{1-5}\end{array}$

Now,

$\displaystyle\bullet\sf\:\sum\:f_i\:d_i\:=\:-\:350\\\\\\\bullet\sf\:\sum\:f_i\:=\:25\\\\\\\pink{\sf\:\overline{d}\:=\:\dfrac{\sum\:f_i\:d_i}{\sum\:f_i}}\\\\\\\implies\sf\:\overline{d}\:=\:-\:\cancel{\dfrac{350}{25}}\\\\\\\implies\boxed{\red{\sf\:\overline{d}\:=\:-\:14}}$

Now,

$\displaystyle\pink{\sf\:Mean\:\overline{X}\:=\:A\:+\:\overline{d}}\sf\:\:\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:\overline{X}\:=\:225\:+\:(\:-\:14\:)\\\\\\\implies\sf\:\overline{X}\:=\:225\:-\:14\\\\\\\implies\boxed{\red{\sf\:\overline{X}\:=\:211}}$

Hence,

The mean daily expenditure on food is Rs. 211.

Answer 2

Step-by-step explanation:

food of 25 households in a locality.

150-200

Daily expenditure 100 - 150

(in)

200-250

250 - 300

300-350

4

5

12

2.

2.

Number of

households

Find the mean daily expenditure on food by assumed mean