Statistical Techniques for Transportation Engineering

Index number for 1945 by

1. $\begin{array}{ll}\text{Laspeyre}’\mathrm{s}\mathrm{method}\hfill & =\frac{\mathrm{\Sigma }{p}_0{q}_0}{\mathrm{\Sigma }{p}_1{q}_1}\times 100\hfill \\ =\frac{610}{240}\times 100=254.2\hfill \end{array}$

2. $\begin{array}{ll}\text{Paasche}’\mathrm{s}\mathrm{method}\hfill & =\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\times 100\hfill \\ =\frac{426}{170}\times 100=250.6\hfill \end{array}$

3. $\begin{array}{ll}\mathrm{Bowley}\mathrm{method}\hfill & =\frac{\left[\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}+\frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}\right]}{2}\times 100\hfill \\ =\frac{2.542+2.506}{2}\times 100=252.4\hfill \end{array}$

4. $\begin{array}{ll}\mathrm{Marshall}\text{Edgeworth}’\mathrm{s}\mathrm{index}\mathrm{number}\hfill & =\frac{\mathrm{\Sigma }{p}_1{q}_0+\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_0+\mathrm{\Sigma }{p}_0{q}_1}\times 100\hfill \\ =\frac{610+426}{240+170}\times 100=252.7\hfill \end{array}$

5. $\begin{array}{ll}\text{Fisher}’\mathrm{s}\mathrm{index}\mathrm{number}=p_{01}\hfill & =\sqrt{\frac{\mathrm{\Sigma }{p}_1{q}_0}{\mathrm{\Sigma }{p}_0{q}_0}\times \frac{\mathrm{\Sigma }{p}_1{q}_1}{\mathrm{\Sigma }{p}_0{q}_1}}\times 100\hfill \\ =\sqrt{\frac{610}{240}\times \frac{\mathrm{426\; ...}}{}}\hfill \end{array}$