Haryana Police Constable Model Paper 7

Given:
Group of 6 people having weights $45,50,65,72,63,35$ (in kgs)
Formula Used:
$\mathrm{Mean}=\frac{\mathrm{sum}\mathrm{of}\mathrm{observations}}{\mathrm{number}\mathrm{of}\mathrm{observations}}$
Standard deviation $=\sqrt{\left[\frac{\left(\mathrm{\Sigma }{\mathrm{x}}^2\right)}{\mathrm{N}}\right]}$ , where $\mathrm{\Sigma }{\mathrm{x}}^2$ } is the summation of the square of deviation of all observations from Mean.
Calculation;
Sum of all observations $=\left(45+50+65+72+63+35\right)=330$
Mean $=\frac{330}{6}$ = 55 $\mathrm{\Sigma }{\mathrm{x}}^2=\left(100+25+100+289+64+400\right)$
$\Rightarrow \mathrm{\Sigma }{\mathrm{x}}^2=978$
Standard Deviation $\left(\mathrm{\sigma }\right)=\sqrt{\left(\frac{978}{6}\right)}$ $=\sqrt{163}$
∴ The standard deviation of given data set of weights is $\sqrt{163}$ .