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The mean of the n observations \( \Large x_{1},\ x_{2},\ x_{3}.....,\ x_{n} \) be \( \Large \overline{x} \). Then, the mean of n observations \( \Large 2x_{1}+3,\ 2x_{2}+3,\ 2x_{3}+3,.......2x_{n}+3 \) is


A) \( \Large 3\overline{x}+2 \)

B) \( \Large 2\overline{x}+3 \)

C) \( \Large \overline{x}+3 \)

D) \( \Large 2\overline{x} \)

Correct Answer:
B) \( \Large 2\overline{x}+3 \)

Description for Correct answer:
Given that, \( \Large \overline{x} = \frac{x_{1}+x_{2}+...+x_{4}}{n} \)

=> \( \Large n\overline{x} = x_{1}+x_{2}+...+x_{n} \)

Now, required mean = \( \Large \frac{2x_{1}+3+...+2x_{n}+3}{n} \)

= \( \Large \frac{2 \left(x_{1}+x_{2}+...+x_{n}\right)+3n}{n} \)

= \( \Large \frac{2n\overline{x}+3n}{n} = 2\overline{x}+3 \)

Part of solved Statistics questions and answers : >> Elementary Mathematics >> Statistics




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