An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: Firm A Firm B No. of wages earners 586 684 Mean of monthly wages Rs. 5253 Rs. 5253 Variance of the distribution of wages 100 121 Which firm A or B pays to larger mount as monthly wages? Which firm A or B shows greater variability in individual wages?

Explanation

This is a case for comparing the variability
`therefore` We will calculate the coefficient of variance for each series
`because` variance of the distribution of wages in firm `A(sigma_1^2)=100`
`therefore` Standard deviation of wages =`(sigma_1) =sqrt100=10`
Similarly standard deviation of wages in firm `B(sigma_2)=sqrt121=11`
`therefore` C.V. (`1^"st"` distribution )=`sigma_1/x_1xx100=10/5253xx100`
C.V. (`2^"nd"` distribution )=`sigma_2/x_2xx100=11/5253xx100`
`because` Means of `1^"st"` and `2^"nd"` distribution are same
`therefore` C.V. of `2^"nd"` distribution is greater,
Total wages for firm A =586 x 5253
=Rs. 3078258
Total wages for firm B =Rs. 648 x 5253
=Rs.3403944
`therefore` Firm B pays larger amount