Question

There are four rain gauge stations existing in the catchment of a river. The average annual rainfall values at these stations are 800, 620, 400 and 540 mm. How many more gauges are required to be installed, if it is desired to limit the error in the mean value of rainfall in the catchment to 10%?

• A. 5
• B. 6
• C. 4
• D. 3

Answer 1

The correct option is A 5

(i) Mean rainfall
$\left(\overline{P}\right)=\frac{\Sigma P}{n}=\frac{800+620+400+540}{4}=590mm$

(ii) Standard deviation , $\sigma =\sqrt{\frac{\Sigma (P-\overline{P}{)}^2}{n-1}}=166.93mm$

(iii) Coefficient of variation , $C_v=\frac{100\sigma }{\overline{P}}=\frac{100\times 166.93}{590}=28.29$

(iv) Optimum number of rain gauges , $\left(N\right)={\left(\frac{C_v}{ϵ}\right)}^2={\left(\frac{28.29}{10}\right)}^2=8.005=9Nos$

(v) Additional gauges required to be installed
$=9-\text{Existing rain gauges}$
$=9-4=5$