Question

Find the median wages for the following frequencies distribution:

Wages per day (in Rs)	61-70	71-80	81-90	91-100	101-110	111-120
No. of women workers	5	15	20	30	20	8

Answer 1

Converting the given data into exclusive form, we get:

Class	Frequency(f)	Cumulative frequency
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=∑f=98

$$\begin{gathered} N=98 \\ \Rightarrow \frac{N}{2}=49 \\ \text{The cumulative frequency just greater than 49 is 70 and the corresponding class is 90}\text{.5-100}\text{.5.} \\ \text{Thus, the median class is 90}\text{.5-100}\text{.5.} \\ \mathrm{Now},l=90.5,h=10,f=30,cf=\text{c}\text{.f}\text{. of preceding class = 40 and}\frac{N}{2}=49 \\ \therefore \text{Median,}M=l+\{h\times \frac{(\frac{N}{2}-cf)}{f}\} \\ \text{=90}\text{.5+}\{10\times \frac{(49-40)}{30}\} \\ \text{=90}\text{.5+3} \\ \text{=93}\text{.5} \\ \text{Hence, median wages = Rs 93}\text{.50} \end{gathered}$$