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State True/ False:

The table below shows the daily expenditure on food of 30 households in a locality. Then the median of daily expenditure on food is Rs.208.2.

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 B.

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Detailed Solution

Consider the given table,

DAILY EXPENDITURE (in Rs.)	NUMBER OF HOUSEHOLDS
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.	$f_{i}$	c.f.
100-150	6	6
150-200	7	13
200-250	12	25
250-300	3	28
300-350	2	30
	$\sum f_{i} = 30$

Here, we have,
N=

\sum f_{i}

= 30

\frac{N}{2} = \frac{30}{2}

= 15
We can observe that the cumulative frequency just greater than 15 is 25 and the corresponding class is

200 − 250

.
Therefore, the median class is

200 − 250

.
We know that, the formula for median is,

M = l + h × N 2 − c f f

, where,

l =

the lower limit of the median class,

N = ∑ frequency

, and

cf =

cumulative frequency of the class just preceding the median class.
Note that, here

l = 200

N = 30

f = 12

h = 50

c . f = 13

Therefore, the median is,

= 200 + 50 × 15 − 13 12 = 200 + 8.33 = 208.33

Hence, the median of daily expenditure on food is Rs.208.33.
Thus, the given statement is false.
Therefore, option 2 is correct.

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