Question

There are four raingauge stations existing in the catchment of a river. The average annual rainfall values at these stations are 780, 640, 400, 520 mm. Allowable percentage error in mean value of rainfall is 10%. The optimum number of rain gauges in the catchment should be ________.

• A. 8

Answer 1

The correct option is A 8
Mean rainfall,

$\overline{P}=\frac{P_1+P_2+P_3+P_4}{4}$

$=\frac{780+640+400+520}{4}=585mm$

Standard deviation,

${\sigma }_{n-1}=\sqrt{\frac{\sum _{i=1}^4(P_i-\overline{P}{)}^2}{n-1}}$

$=\sqrt{\frac{(780-585{)}^2+(640-585{)}^2+(400-585{)}^2+(520-585{)}^2}{3}}$

$=162.788$

Coefficient of variation,

$C_V=\frac{{\sigma }_{n-1}}{\overline{P}}\times 100=\frac{162.788}{585}\times 100=27.827\%$

$\therefore$ Optimum number of rain gauges,

$N={\left(\frac{C_V}{\in }\right)}^2={\left(\frac{27.827}{10}\right)}^2=7.743\underset{–}{\sim }8$

Hence, 8 rain gauges are required.