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The following table shows the daily wages of workers in a factory:

Daily Wages (in Rs.)
Number of workers
0-100
40
100-200
32
200-300
48
300-400
22
400-500
8

What will be the median of the given data?

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Rs.206.25

Rs.306

Rs.206.15

Rs.305.36

answer is A.

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Detailed Solution

Given table shows the daily wages of workers in a factory:

Daily Wages (in Rs.)	Number of workers
0-100	40
100-200	32
200-300	48
300-400	22
400-500	8

Formula used for median:

M e d i a n = l + h × N 2 − c f f

,
where,

l

=lower limit of the median class,

h

=size of the median class,

f

= frequency of the median class,

N

= sum of frequencies and

c f

=cumulative frequency of the class just preceding the median class.
The frequency distribution table will be,

Daily Wages (in Rs.)	Number of workers	Cumulative Frequency
0-100	40	40
100-200	32	40+32=72
200-300	48	72+48=120
300-400	22	120+22=142
400-500	8	142+8=150

Here, N = 150.

N 2 = 1502 = 75

The cumulative frequency just greater than 75 is 120 and the corresponding class is

200 − 300

.
Therefore, the median class is

200 − 300

∴ l = 200, h = 100, f = 48, N = 150 and c f = 72

Calculating the median, we get,

Median = 200 + 100 × 1502 − 72 48 Median = 200 + 100 × 75 − 72 48 Median = 200 + 100 × 348 M e d i a n = 200 + 100 × 0.0625 M e d i a n = 200 + 6.25 M e d i a n = 206.25

Thus, the median of given data is Rs.206.25.
Therefore, the correct option is 1.

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