The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively.

Question

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where $p
e0$ and $q
e0$. If the new mean and new s.d. become half of their original values, then q is equal to:

Accepted Answer

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

Solutions · 1