\(\overset { = }{ X } =\frac { \sum { \overset { - }{ X } } }{ number\ of\ samples } =\frac { 1971 }{ 6 } =328.5\quad \quad \overset { - }{ R } =\frac { \sum { R } }{ n } =\frac { 162 }{ 6 } =27\)
The control limits for \(\overset {-}{X}\) chart is
\(UCL=\overset { = }{ X } +{ A }_{ 2 }\overset { - }{ R } =328.5+0.483(27)=341.54\)
\(CL=\overset { = }{ X } =328.5\)
\(LCL=\overset { = }{ X } -{ A }_{ 2 }\overset { - }{ R } =328.5+0.483(27)=315.45\)

Smce \(\sum\)X = 0, a =\(\frac {\sum Y}{n}\) = \(\frac {244}{5}\) = 48.8
b = \(\frac {\sum XY}{\sum X^2}\) = \(\frac {20}{10}\) = 2
∴ The required equation of the straight line trend is given by
Y = a + bX  \(\Rightarrow \) Y = 48.8 + 2X
\(\Rightarrow \) Y = 48.8 +2 (X - 1994) .... (1)
∴ Number of salesmen in 1997 is put X = 1997 in (1)
∴ Y = 48.8 + 2 (1997 - 1994) 
= 48.8 + 2 (3) 
= 48.8 + 6 = 54.8
∴  Number of salesmen in 1997 is 54.8

Grand Average =  \(= \frac {17.6+ 20.3+ 18+ 14.3 + 14+ 17 + 20.6+ 18+ 17.3 + 17 + 16.3+ 17.6}{12}\) = \(\frac {208}{12}\) = 17.33
S.I for Jan = \(\frac {17.6}{17.33}\) × 100 = 101.56
S.I for Feb = \(\frac {20.3}{17.33}\) × 100 = 117.14
S.I for Mar = \(\frac {18}{17.33}\) × 100 = 103.87
S.I for April = \(\frac {14.3}{17.33}\) × 100 = 82.51
S.I for May = \(\frac {14}{17.33}\) × 100 = 80.78
S.I for June = \(\frac {17}{17.33}\) × 100 = 98.10
S.I for July = \(\frac {20}{17.33}\) × 100 = 118.87
S.I for Aug = \(\frac {20.6}{17.33}\) × 100 = 103.87
S.I for Sep = \(\frac {17.3}{17.33}\) × 100 = 99.83
S.I for Oct = \(\frac {17}{17.33}\) × 100 = 98.10
S.I for Nov = \(\frac {16.3}{17.33}\) × 100 = 94.06
S.I for Dec = \(\frac {17.6}{17.33}\) × 100 = 101.56

 Since \(\sum X = 0, a = \frac{\sum Y}{n}\) = \(\frac {270}{5}\) = 54
b = \(\frac {\sum XY}{\sum X^2} = \frac {54}{10}\) = 5.4
∴  The required equation of the straight line trend is given by Y  = a +bX  
\(\Rightarrow \) Y = 54 + 5.4 (x - 2002)
The trend values can be obtained as follows: 
When X = 2000, Y_t = 54 + 5.4 (2000 - 2002)
= 54 + 5.4 (-2) = 43.2
When X = 2001, Y_t = 54 + 5.4 (2001 - 2002)
= 54 + 5.4(-1) = 48.6
When X = 2002, Y_t = 54 + 5.4 (2002 - 2002)
= 54
When X = 2003, Y_t = 54 + 5.4 (2003 - 2002) 
= 54 + 5.4 = 59.4
When X = 2004, Y_t = 54 + 5.4 (2004 - 2002)
= 54 + 5.4 (2) = 64.8

Grand average = (3.72 + 4.16 + 3.76 + 4.16)/4 = 3.95
Seasonal Index (S.I) for I quarter = (Average of I quarter)/(Grand Average) \(\times\) 100
S.I. for I quarter = 3.72/3.95 \(\times\) 100 = 94.1772 
S.I. for II quarter = 4.16/3.95 \(\times\) 100 = 105.3165 
S.I. for III quarter = 3.76/3.95 \(\times\) 100 = 95.1899 
S.I. for IV quarter = 4.16/3.95 \(\times\) 100 = 105.3165 
Thus we obtain the average seasonal movement.