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Mean

The mean of s...

Question

The mean of set of $30$ observations is $75.$ If each of the observations is multiplied a non-zero number $λ$ and then each of them is decreased by $25$ , their mean remains same then $λ = \frac{4}{3}$ .

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Solution

$\begin{matrix} F o r t h e v a l u e s x_{1}, x_{2}, . . . x_{n} o f t h e v a r i a n t x t h e a r i t h m e t i c m e a n i s g i v e n b y ¯ ¯ ¯ x = \frac{x_{1} + x_{2} + x_{3} + . . . . . + x_{n}}{n} I n t h e g i v e n q u e s t i o n T h e n e w m e a n = 75 λ - 25 a l s o, w e h a v e 75 λ - 25 = 75 ∴ λ = \frac{4}{3} H e n c e, w e g e t t h e r e q u i r e d a n s w e r . \end{matrix}$

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