QJEEM20Ma0bfe: JEE Main 2020 Mathematics - Class 11 JEEM20Ma0bfe Solution: The mean and the standard deviation (s.d.) of 10 observations…

Let observations are x₁, x₂, ...., x₁₀

Here mean = 20 and standard deviation(S.D) = 2

When each of these 10 observations is multiplied by p then new observations are px₁, px₂, ....., px₁₀
and new mean = 20p and new standard deviation(S.D) = 2|p|

Now when Reduced by q then new observations are
px₁ - q, px₂ - q, ....., px₁₀ - q

and new mean = 20p - q and new standard deviation(S.D) = 2|p|

Given 20p - q = ${{20} \over 2}$ = 10
and 2|p| = ${2 \over 2}$ = 1

$\Rightarrow$ p = $\pm$ ${1 \over 2}$

If p = ${1 \over 2}$ then q = 0 (not possible as given q $\ne$ 0)

If p = - ${1 \over 2}$ then q = -20