Question

If mean of the n observations ${x_1, x_2, x_3,... x_n}$ be $\bar{x}$ , then the mean of n observations ${2x_1 + 3, 2x_2 + 3, 2x_3 + 3, ...., 2x_{n} + 3}$ is

• A. $\ce{3 \bar{x} +2}$
• B. $\ce{2 \bar{x} + 3}$
• C. $\ce{ \bar{x} + 3 }$
• D. $\ce{2 \bar{x} }$

Answer 1

Answer: (B)

$\ce{2 \bar{x} + 3}$

Answer 2

Required mean = ${\frac{1}{n} \displaystyle\sum_{i=1}^{n} (2x_{i} + 3)}$ = {\frac{2}{n} } \bigg( { \displaystyle\sum_{i=1}^{n} x_{i}} \bigg) + {\frac{3n}{n}} = 2 \bigg\\{ { \frac{1}{n} } \bigg( {\displaystyle\sum_{i=1}^{n} x_{i} } \bigg) \bigg\\} + 3 ${ = 2 \bar{x} + 3}$