JEE Main 2020 — Statistics Question with Solution

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 = $$\frac{20}{2}$$ = 10
and 2|p| = $$\frac{2}{2}$$ = 1

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

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

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