1. Tardigrade
  2. Question
  3. Mathematics
  4. 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 Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

Statistics

Solution:

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$