The mean of a set of observations is barx. If each observation is divided by α,(α ≠ 0) and then is increased by 10 , then the mean of the new set is

Question

The mean of a set of observations is barx. If each observation is divided by α,(α ≠ 0) and then is increased by 10 , then the mean of the new set is (A) ( barx/α) (B) ( overline x +10/α) (C) ( barx+10 α/α) (D) (α barx+10/α)

Tardigrade Admin · Accepted Answer

Let the set of n observations x 1, x 2, ldots ldots x n ∴ overline x =( Sigma x 1/ n ) Mean of new set =( Sigma(( x 1/α)+10)/ n )=(1/α) (∑ x 1/ n )+(10 n / n )=( overline x +10 α/α)

Q. The mean of a set of observations is $\overset{x}{ˉ}$ . If each observation is divided by $α, (α \neq = 0)$ and then is increased by $10$ , then the mean of the new set is

$\frac{x ˉ}{α}$

$\frac{x + 10}{α}$

$\frac{x ˉ + 10 α}{α}$

$\frac{α x ˉ + 10}{α}$

Let the set of $n$ observations $x_{1}, x_{2}, \dots\dots x_{n}$
$∴ \overline{x} = \frac{Σ x _{1}}{n}$
Mean of new set $= \frac{Σ ( \frac{x _{1}}{α} + 10 )}{n} = \frac{1}{α} \frac{\sum x _{1}}{n} + \frac{10 n}{n} = \frac{x + 10 α}{α}$

Q. The mean of a set of observations is xˉ. If each observation is divided by α,(α=0) and then is increased by 10 , then the mean of the new set is

αxˉ​

αx+10​

αxˉ+10α​

ααxˉ+10​