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The mean of a set of 30 observations is 75 . If each other observation is multiplied by a nonzero number $\lambda$ and then each of them is decreased by 25 , their mean remains the same. The $\lambda$ is equal to
equal to $\{0\}$
Options:
equal to $\{0\}$
Solution:
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Verified Answer
The correct answer is:
$\frac{4}{3}$
$\frac{4}{3}$
As mean is a linear operation, so if each observation is multiplied by $\lambda$ and decreased by 25 then the mean becomes 75 $\lambda-25$.
According to the question,
$$
75 \lambda-25=75 \Rightarrow \lambda=\frac{4}{3}
$$
According to the question,
$$
75 \lambda-25=75 \Rightarrow \lambda=\frac{4}{3}
$$
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