Question

Given the following data on monthly wages of 1000 workers, frequency of two class interval are missing. Locate
these if the Median of the series is 56.
Wages (in Rs) 20-30
30-40
40-50
50-60
60-70
70-80
Number of Workers
60
60
?
200
?
285​

Answer 1

Wages  frequencycumulative frequency20-30606030-406012040-50f1120+ f150-60200 320 + f160-70f2320 + f1 +f270-80285605 + f1 +f2Total10001000

605 + f1 + f2 = 1000

f1 + f2 = 395 --------------------- (i)

As median is 56 median class is 50-60

Median = l + n/2 - cf / f * i

56 = 50 + 1000/2 - ( 120 + f1 ) / 200 * 10

56 = 50 + 500 - 120 - f1 / 20

56 = 1000 + 380 - f1 / 20

56 * 20 = 1380 - f1

1120  = 1380 - f1

f1 = 260

substituting value in (i)

f1 + f2 = 395

260 + f2 = 395

f2 = 135

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