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Home  >>  CBSE XI  >>  Math  >>  Statistics
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An analysis of monthly wages paid to workers in two firms A and B , belonging to the same industry, gives the following results. (i) Which firm A and B pays larger amount as monthly wages. (ii) which firm A or B shows greater variability in individual wages?

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For Firm A,
Step 1:
Number of wages earners = 586 (given)
Mean of monthly wages $=\bar {X} =Rs. 5253$ (given)
Amount paid by the firm A= Number of wage earners $\times $ mean of monthly wages.
$\qquad= 586 \times 5253$
$\qquad= Rs. 3078258$
Step 2:
Variance of the distribution of wages=100(given)
Standard deviation $=\sqrt{variance}$
$\qquad= \sqrt{100}$
$\qquad=10$
Step 3:
Coefficient of variation $=\large\frac{\sigma}{\bar{X}} $$ \times 100$
$\qquad= \large\frac{10}{5253}$
$\qquad= \large\frac{1000}{5253}$
$\qquad= 0.19$
For firm B
Step 1:
Number of wages earners = 648 (given)
Mean of monthly wages $=Rs. 5253$ (given)
Amount paid by the firm B= Number of wage earners $\times $ mean of monthly wages.
$\qquad= 648 \times 5253$
$\qquad= Rs. 3403944$
Step 2:
Variance of the distribution of wages=121(given)
Standard deviation $=\sqrt{variance}$
$\qquad= \sqrt {121}$
$\qquad=11$
Step 3:
Coefficient of variation $=\large\frac{\sigma}{\bar{X}} $$ \times 100$
$\qquad= \large\frac{11}{5253} \times 100$
$\qquad= \large\frac{1100}{5253}$$=0.21$
COMPARISON:
(i) Monthly wages paid by firm $A= Rs. 3078258$
Monthly wages paid by firm $B= Rs. 3403944$
$\therefore$ Firm B pays larger amount of monthly wages.
(ii) Variability of the firm depends upon coefficient of variation.
Higher the coefficient of variation, higher the variability
$\therefore $ coefficient of variation of firm B is higher .
Hence , firm B shows greater variability in individual wages.
answered Jul 1, 2014 by meena.p
 

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