Question

A catchment has six rainguage stations. In a year, the annual rainfall record by the gauges are as follows

Station	A	B	C	D	E	F
Rainfall (cm)	76	85	101	130	88	110

For the 12% error in the estimation of mean rainfall, the optimum number of stations required in the catchment are

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

As per given data,
Number of stations : h = 6
mean precipitation value ,
$\overline{p}=\frac{\sum _{i=1}^n{p}_i}{n}=98.33cm$

Standard deviation for the data,
${\sigma }_{n-1}=\sqrt{\left[\frac{\sum _{i=1}^n(p_i-\overline{p}{)}^2}{n-1}\right]}$

$=\sqrt{\frac{1929.333}{5}}=19.64$

Optimum number of raingauges,
$N={\left(\frac{C_v}{ϵ}\right)}^2$
Now,
$C_v=\text{Coefficient of variation}$

$=\frac{100\times {\sigma }_{n-1}}{\overline{p}}=\frac{100\times 19.64}{98.33}=19.97$

$\therefore N={\left(\frac{C_v}{ϵ}\right)}^2={\left(\frac{19.97}{12}\right)}^2=2.769\simeq 3$

3 station are required