Question

The following distribution gives the number of accidents met by 160 workers in a factory during a month.
No of accidents (x): 0 1 2 3 4
No of workers (f): 70 52 34 3 1

Find the average number of accidents per worker.

Answer 1

ASSUMED MEAN METHOD :  

In this method, first of all, one among xi 's is chosen as the assumed mean denoted  by ‘A’. After that the difference ‘di’ between ‘A’ and each of the xi's i.e di = xi - A is calculated .  

ARITHMETIC MEAN =  A +  Σfidi / Σfi

[‘Σ’ Sigma means ‘summation’ ]

★★ We may take Assumed mean 'A’ to be that xi which lies in the middle of x1 ,x2 …..xn.

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfidi = - 187 ,Σfi = 160

Let the assumed mean, A = 2

ARITHMETIC MEAN =  A +  Σfidi / Σfi

ARITHMETIC MEAN =  2 + (- 187 / 160)

= 2 - 187 / 160

= 2 - 1.168

= 0.83

ARITHMETIC MEAN = 0.83  

Hence, the average number of accidents per worker is 0.83 .  

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Average = no of accidents / no of workers
Average = x / f
= 1 + 2 +3 + 4 + 0 / 70 + 52+ 34+ 3+1
= 10/134
= 0.074 accidents per worker.