Consider 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?

This question was previously asked in
AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov, 2022 Shift 2)
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  1. 18
  2. 20
  3. 16
  4. 15

Answer (Detailed Solution Below)

Option 2 : 20
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Detailed Solution

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Given:

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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