Question

The following table shows classification of number of workers and the number of hours they work in a software company. Find the median of the number of hours they work.

Daily No. of hours	8 - 10	10 - 12	12 - 14	14 - 16
Number of workers	150	500	300	50

Answer 1

Class (Number of working hours)	Frequency (Number of workers) fi	Cumulaive frequency less than the upper limit
8 - 10	150	150
10 - 12 (Median Class)	500	650
12 - 14	300	950
14 - 16	50	1000
	$N=1000$

From the above table, we get
L (Lower class limit of the median class) = 10
N (Sum of frequencies) = 1000
h (Class interval of the median class) = 2
f (Frequency of the median class) = 500
cf (Cumulative frequency of the class preceding the median class) = 150
Now, Median = $L+\left(\frac{{\displaystyle \frac{N}{2}-cf}}{f}\right)\times h$
​$$\begin{gathered} =10+\left(\frac{{\displaystyle \frac{1000}{2}-150}}{500}\right)\times 2 \\ =10+1.4 \\ =11.4\mathrm{hours} \end{gathered}$$
Hence, the median of the number of hours they work is 11.4 hours.