Question

Find the median wages for the following frequency distribution: $\begin{array}{ccccccc}\text{Wages per day}& 61-70& 71-80& 81-90& 91-100& 101-110& 111-120\\ \text{(in Rs.)}& & & & & & \\ \text{No. of women}& 5& 15& 20& 30& 20& 8\\ \text{workers}& & & & & & \end{array}$

Answer 1

The given series is of inclusive form. Converting it into exclusive form and preparing the cumulative frequency table, we get

Wages per day (in Rs.)	Frequency fi	C.F
60.5-70.5	5	5
70.5-80.5	15	20
80.5-90.5	20	40
90.5-100.5	30	70
100.5-110.5	20	90
110.5-120.5	8	98
	N=∑fi=98

N =98

=> N/2 = 49

Now,

The cumulative frequency just greater than 49 is 70 and corresponding class is 90.5-100.5.

Thus, the median class is 90.5-100.5

I = 90.5, h = 10, f = 30, c = C.F. preceding median class = 40 and N/2 = 49

Median = I+[h×(N/2−cf)/f]
=90.5+[10×(49−40)/30]

= 90.5+3 = Rs. 93.5

Hence, median is Rs. 93.5