Value of encouraging more and more students to participate by announcing a cash prize is shown.

Taking assumed mean, a = 90
Let us make the following table from the given data.

Here, \(\Sigma { { f }_{ i }d }_{ i }\) = 21, \(\Sigma { f }_{ i }\) = 48, \(\Sigma { f }_{ i }{ d }_{ i }^{ 2 }\) = 6763
\(\therefore \)  Mean, \(\overline { x } =90+\frac { 21 }{ 48 } \)     \(\left[ \because \overline { x } =a+\frac { \Sigma { { f }_{ i }d }_{ i } }{ \Sigma { { f }_{ i } } } \right] \) 
= 90 + 0.44 = 90.44
and variance, \({ \sigma }^{ 2 }\) = \(\frac { \Sigma { { f }_{ i }d }_{ i }^{ 2 } }{ \Sigma { { f }_{ i } } } \) - \({ \left( \frac { \Sigma { { f }_{ i }d }_{ i } }{ \Sigma { { f }_{ i } } } \right) }^{ 2 }\) 
= \(\frac { 6763 }{ 48 } -{ \left( \frac { 21 }{ 48 } \right) }^{ 2 }\) 
= 140.896 - 0.191
= 140.705 (approx)
\(\Rightarrow \sigma =\sqrt { 140.705 } =11.86\)                         
Now,  \(\overline { x } -\sigma \)  = 90.44 - 11.86
= 78.58.
and \(\overline { x } +\sigma \)  =  90.44 + 11.86
= 102.30
\(\therefore \)  The number of children whose scores lies between \(\overline { x } -\sigma \) and \(\overline { x } +\sigma \)  i.e. between 78.50 and 102.30.
= 4 + 5 + 6 + 5 + 4 + 4 + 3 = 31
Hence, percentage of these children = \(\frac { 31 }{ 48 } \times 100\) = 64.58 (approx).

For Firm A
Number of wages earners = 586
Mean of monthly wages,\(\overline { x } \) = Rs. 5253
Amount paid by firm A = Rs \(\left( 586\times 5253 \right) \) = Rs.3078258
Variance of distribution of wages = 100
\(\therefore \) Standard deviation, \(\sigma \) = \(\sqrt { variance } =\sqrt { 100 } =10\) 
Coefficient of variance \(=\frac { \sigma }{ x } \times 100\)  
\(=\frac { 10 }{ 5253 } \times 100=0.19\).
For Firm B
Number of wages earners = 648
Mean of monthly wages,\(\overline { x } \) = Rs. 5253
Amount paid by firm B =Rs.\(\left( 648\times 5253 \right) \) = Rs.3403944
Standard deviation \(=\sqrt { 121 } =11\)  
\(\therefore \)  Coefficient of variance\(=\frac { \sigma }{ x } \times 100\)\(=\frac { 10 }{ 5253 } \times 100=0.21\).
Value of motivating employees by giving financial incentives is addressed by the firm.

For Firm A
Number of wages earners = 586
Mean of monthly wages,\(\overline { x } \) = Rs. 5253
Amount paid by firm A = Rs \(\left( 586\times 5253 \right) \) = Rs.3078258
Variance of distribution of wages = 100
\(\therefore \) Standard deviation, \(\sigma \) = \(\sqrt { variance } =\sqrt { 100 } =10\) 
Coefficient of variance \(=\frac { \sigma }{ x } \times 100\)  
\(=\frac { 10 }{ 5253 } \times 100=0.19\).
For Firm B
Number of wages earners = 648
Mean of monthly wages,\(\overline { x } \) = Rs. 5253
Amount paid by firm B =Rs.\(\left( 648\times 5253 \right) \) = Rs.3403944
Standard deviation \(=\sqrt { 121 } =11\)  
\(\therefore \)  Coefficient of variance\(=\frac { \sigma }{ x } \times 100\)\(=\frac { 10 }{ 5253 } \times 100=0.21\). 
Coefficient of variation of wages of Firm A = 0.19
Coefficient of variation of wages of Firm B = 0.21.

For Firm A
Number of wages earners = 586
Mean of monthly wages,\(\overline { x } \) = Rs. 5253
Amount paid by firm A = Rs \(\left( 586\times 5253 \right) \) = Rs.3078258
Variance of distribution of wages = 100
\(\therefore \) Standard deviation, \(\sigma \) = \(\sqrt { variance } =\sqrt { 100 } =10\) 
Coefficient of variance \(=\frac { \sigma }{ x } \times 100\)  
\(=\frac { 10 }{ 5253 } \times 100=0.19\).
For Firm B
Number of wages earners = 648
Mean of monthly wages,\(\overline { x } \) = Rs. 5253
Amount paid by firm B =Rs.\(\left( 648\times 5253 \right) \) = Rs.3403944
Standard deviation \(=\sqrt { 121 } =11\)  
\(\therefore \) Coefficient of variance\(=\frac { \sigma }{ x } \times 100\)\(=\frac { 10 }{ 5253 } \times 100=0.21\).
Monthly wages paid by firm A = Rs.3078258
Monthly wages paid by firm B = Rs.3403944.