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The mean of n observations is \( \Large \overline{x} \). If one observation \( \Large x_{n+1} \) is added, then the mean remains same. The value of \( \Large x_{n+1} \) is:


A) 0

B) 1

C) n

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

Correct Answer:
D) \( \Large \overline{x} \)

Description for Correct answer:

Let \( \Large x_{1},x_{2},x_{3},.... x_{n} \) be n observations

\( \Large \bar{x} = \frac{ \Sigma x_{i}  }{n} \)

New mean = \( \Large \frac{\Sigma x_{i} + \Sigma _{n + 1}}{n + 1} \)

According to the question  \( \Large \bar{x} = \frac{\Sigma x_{i} + \Sigma _{n + 1}}{n + 1} \)


\( \Large  \left( n + 1\right)\bar{x} = n\bar{x} + x_{n + 1}  \)

\( \Large x_{n + 1} = \bar{x} \)


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




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