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?

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:

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.