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Question

The following table shows the daily wages of workers in a factory:
Daily eages (in )0100100200200300300400400500Number of workers403248228
Find the median daily wage income of the workers.

A

₹202.25
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B

₹204.25
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C

₹206.25
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D

₹208.25
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Solution

The correct option is C
₹206.25

We prepare the cumulative frequency table, as shown:

Daily wages Number of workers Cumulative frequency
0-100 40 40
100-200 32 72
200-300 48 120
300-400 22 142
400-500 8 150
N=Σf=150

N= 150

⇒N/2 = 75

The cumulative frequency greater than 75 is 120 and the corresponding class is 200-300.

Thus the median class is 200-300.

Therefore, l=200, h = 100, f = 48,
c.f. of preceding class = 72 and N/2=75

Median,M=l+((N/2−cf) /f)×h
Median=200+((75−72)/48 )×100
Median=200+6.25
Median=206.25

Hence, the median daily wage income of the workers is ₹206.25 .


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