If mean of the n observations x1, x2, x3,... xn be barx , then the mean of n observations 2x1 + 3, 2x2 + 3, 2x3 + 3, ...., 2xn + 3 is

Question

If mean of the n observations x1, x2, x3,... xn be barx , then the mean of n observations 2x1 + 3, 2x2 + 3, 2x3 + 3, ...., 2xn + 3 is (A) 3 barx +2 (B) 2 barx + 3 (C)  barx + 3  (D) 2 barx

Tardigrade Admin · Accepted Answer

Required mean = (1/n) displaystyle∑i=1n (2xi + 3) = (2/n) ( displaystyle∑i=1n xi ) + (3n/n) = 2 (1/n) ( displaystyle∑i=1n xi ) + 3 = 2 barx + 3

Q. If mean of the n observations $x_{1}, x_{2}, x_{3}, ... x_{n}$ be $\overset{x}{ˉ}$ , then the mean of n observations $2 x_{1} + 3, 2 x_{2} + 3, 2 x_{3} + 3, ...., 2 x_{n} + 3$ is

$3 \overset{x}{ˉ} + 2$

$2 \overset{x}{ˉ} + 3$

$\overset{x}{ˉ} + 3$

$2 \overset{x}{ˉ}$

Required mean = $\frac{1}{n} i = 1 \sum n (2 x_{i} + 3)$
$= \frac{2}{n} (i = 1 \sum n x_{i}) + \frac{3 n}{n} = 2 {\frac{1}{n} (i = 1 \sum n x_{i})} + 3$
$= 2 \overset{x}{ˉ} + 3$

Q. If mean of the n observations x1​,x2​,x3​,...xn​ be xˉ , then the mean of n observations 2x1​+3,2x2​+3,2x3​+3,....,2xn​+3 is

3xˉ+2

2xˉ+3

xˉ+3

2xˉ