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State True/ False:

The table below shows the daily expenditure on food of 30 households in a locality. Then, the mean of daily expenditure on food is Rs.205.

DAILY EXPENDITURE (in Rs.)
NUMBER OF HOUSEHOLDS
100-150
6
150-200
7
200-250
12
250-300
3
300-350
2

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True

False

answer is A.

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Detailed Solution

Consider the given table,

DAILY EXPENDITURE (in Rs.)	NUMBER OF HOUSE HOLDS
100-150	6
150-200	7
200-250	12
250-300	3
300-350	2

The frequency distribution table for the given data is:

C.I.	Mid-value $x_{i}$	$f_{i}$	$x_{i} f_{i}$
100-150	125	6	750
150-200	175	7	1225
200-250	225	12	2700
250-300	275	3	825
300-350	325	2	650
		$\sum f_{i} = 30$	$\sum f_{i} x_{i} = 6150$

We know that, mean (

\underset{̲}{x}

) =

\frac{\sum f_{i} x_{i}}{\sum f_{i}}

Here,

\sum f_{i} x_{i} = 6150

and

\sum f_{i} = 30

.
Therefore,
Mean (

\underset{̲}{x}

\frac{6150}{30}

Mean (

\underset{̲}{x}

)= 205
Hence, the mean of daily expenditure on food is Rs.205.
Thus, the given statement is true.
Therefore, option 1 is correct.

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