Statistics-And-Probability Question 615
Question: The mean of the series $ x_1,x_2,…x_{n} $ is $ \bar{X} $ . If $ x_2 $ is replaced by $ \lambda , $ then what is the new mean?
Options:
A) $ \bar{X}-x_2+\lambda $
B) $ \frac{\bar{X}-x_2-\lambda }{n} $
C) $ \frac{\bar{X}-x_2+\lambda }{n} $
D) $ \frac{n\bar{X}-x_2+\lambda }{n} $
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Answer:
Correct Answer: D
Solution:
[d] Mean of series $ (x_1,x_2,x_3…x_{n}) $ $ \bar{x}=\frac{x_1+x_2+x_3+….x_{n}}{n} $
$ \Rightarrow x_1+x_2+x_3+…x_{n}=n\bar{x} $ Now we will replace $ x_2 $ by so no. of elements in series will not change. New series will include $ \lambda $ and exclude $ x_2 $ Hence new series sum: $ (x_1+x_2+…x_{n})-x_2+\lambda =n\bar{x}+\lambda -x_2 $ Now new mean $ =\frac{n\bar{x}+\lambda -x_2}{n}=\frac{n\bar{x}-x_2+\lambda }{n} $
BETA
