Question
Download Solution PDFConsider the following distribution of daily wages of workers:
Daily wages (in ₹) |
400- 450 | 450-500 | 500-550 | 550-600 | 600-650 |
No. of workers | 6 | 3 | 5 | x | 10 |
If the median daily wages are ₹ 570, then what is the value of x?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Median daily wages = ₹570
Formula used:
Median = l + [(n/2 - cf) / f] × h
Where:
l = lower limit of the median class
n = total frequency
cf = cumulative frequency of the class preceding the median class
f = frequency of the median class
h = class width
Calculation:
The cumulative frequency:
Daily wages (in ₹) | No. of workers (f) | Cumulative frequency (cf) |
400-450 | 6 | 6 |
450-500 | 3 | 9 |
500-550 | 5 | 14 |
550-600 | x | 14 + x |
600-650 | 10 | 24 + x |
Total frequency (n) = 24 + x
Median = 570, which lies in the class 550-600.
Therefore, the median class is 550-600.
Now,
l = 550
n = 24 + x
cf = 14
f = x
h = 50
Substitute the values into the median formula:
Median = l + [(n/2 - cf) / f] × h
570 = 550 + [((24 + x)/2 - 14) / x] × 50
20 = [((24 + x - 28)/2) / x] × 50
20 = [((x - 4)/2) / x] × 50
20 = [(x - 4) / (2x)] × 50
20 = (25(x - 4)) / x
20x = 25x - 100
100 = 5x
x = 20
∴ The value of x is 20.
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