Question

A contractor paid daily wages to the labourers as follows ;find the median wage of the labourers daily wage 200-250,250-300,300-350,350-400,400-450,450-500,500-550 number of labourers 3,4,8,7,6,6,7

Answer 1

Therefore the median wage of the laborers is 416.67.

Step-by-step explanation:

Wage         frequency                      cf

200-250             3                            3

250-300             4                             7

300-350             8                           15

350-400             7                           22

400-450             6                           28 (Median class)

450-500              6                          34

500-550             7                           41

n = total frequency = 41

Median:

Median = $(\frac{n+1}{2} )^{th$ term

            $=(\frac{41+1}{2}) ^{th}$ term

           =24 th term.

The 24 th term belongs to 400-450 class

Therefore Median class is  400-450.

L= lower limit of median class = 400

cf= cumulative frequency of preceding class=22

f = frequency of the median class = 6

c= length of the median class= (450-400)=50

$M=L+\frac{\frac{n+1}{2} -cf}{f} .c$

    $=400+\frac{\frac{41+1}{2} -22}{6}\times 50$

    =416.6666

   ≈416.67

Therefore the median wage of the laborers is 416.67.