​I did not get this question...please this time do answer it and dont ask the exact location....it is the 3rd question of first topic test of chapter statiscs of class 11th

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{a},\left(\mathrm{a}+\mathrm{d}\right),\left(\mathrm{a}+2\mathrm{d}\right),....\left(\mathrm{a}+\mathrm{nd}\right) \mathrm{is} \mathrm{Arithmetic} \mathrm{Progression} \mathrm{of} \mathrm{of} \mathrm{n} \mathrm{terms}. \\ \mathrm{We} \mathrm{know} \mathrm{that}: \\ \mathrm{Sum} \mathrm{of} \mathrm{n} \mathrm{terms} \mathrm{of} \mathrm{an} \mathrm{A}.\mathrm{P}.=\frac{\mathrm{n}}{2}\left(\mathrm{First} \mathrm{term}+\mathrm{Last} \mathrm{term}\right)=\frac{\mathrm{n}}{2}\left(\mathrm{a}+\mathrm{a}+\mathrm{nd}\right) \\ =\frac{\mathrm{n}}{2}\left(2\mathrm{a}+\mathrm{nd}\right) \\ \mathrm{Mean}=\overline{\mathrm{X}}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{n} \mathrm{terms} }{\mathrm{n}}=\frac{\frac{\mathrm{n}}{2}\left(2\mathrm{a}+\mathrm{nd}\right)}{\mathrm{n}}=\frac{2\mathrm{a}+\mathrm{nd}}{2} \\ \mathrm{Now} \mathrm{sum} \mathrm{of} \mathrm{deviations} \mathrm{about} \mathrm{the} \mathrm{mean} \mathrm{is} : \\ \mathrm{S}=\left(\mathrm{a}-\frac{2\mathrm{a}+\mathrm{nd}}{2}\right)+\left(\mathrm{a}+\mathrm{d}-\frac{2\mathrm{a}+\mathrm{nd}}{2}\right)+.....+\left(\mathrm{a}+\left(\mathrm{n}-1\right)\mathrm{d}-\frac{2\mathrm{a}+\mathrm{nd}}{2}\right)+\left(\mathrm{a}+\mathrm{nd}-\frac{2\mathrm{a}+\mathrm{nd}}{2}\right) \\ =\left(\frac{2\mathrm{a}-2\mathrm{a}-\mathrm{nd}}{2}\right)+\left(\frac{2\mathrm{a}+2\mathrm{d}-2\mathrm{a}-\mathrm{nd}}{2}\right)+.....+\left(\frac{2\mathrm{a}+2\mathrm{nd}-2\mathrm{d}-2\mathrm{a}-\mathrm{nd}}{2}\right)+\left(\frac{2\mathrm{a}+2\mathrm{nd}-2\mathrm{a}-\mathrm{nd}}{2}\right) \\ =\left(\frac{-\mathrm{nd}}{2}\right)+\left(\frac{2\mathrm{d}-\mathrm{nd}}{2}\right)+.....+\left(\frac{\mathrm{nd}-2\mathrm{d}}{2}\right)+\left(\frac{2\mathrm{nd}-\mathrm{nd}}{2}\right) \\ =-\left(\frac{\mathrm{nd}}{2}\right)-\left(\frac{\mathrm{nd}-2\mathrm{a}}{2}\right)+.....+\left(\frac{\mathrm{nd}-2\mathrm{d}}{2}\right)+\left(\frac{\mathrm{nd}}{2}\right) \\ \mathrm{As} \mathrm{you} \mathrm{can} \mathrm{see} \mathrm{first} \mathrm{and} \mathrm{last} \mathrm{term} \mathrm{will} \mathrm{cancel} \mathrm{out} \mathrm{each} \mathrm{other}, \mathrm{second} \mathrm{and} \mathrm{second} \mathrm{last} \\ \mathrm{term} \mathrm{will} \mathrm{cancel} \mathrm{out} \mathrm{each} \mathrm{other}. \\ \mathrm{Similarly} \mathrm{all} \mathrm{terms} \mathrm{will} \mathrm{cancel} \mathrm{out} \mathrm{each} \mathrm{o} \\ \Rightarrow \mathrm{S}=0 \\ \mathrm{Option}\left(\mathrm{A}\right) \mathrm{is} \mathrm{correct}. \end{gathered}$$

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