The mean of the series $$x1$$,$$x2$$,…,xn is x¯. If $$x2$$ is replaced by λ, then the new mean is

Correct option is 4nx¯−x2+λn

Questions

The mean of the series $x_{1}, x_{2}, \dots, x_{n} is \bar{x}$ . If x₂ is replaced by $λ$ , then the new mean is

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x¯−x2+λ

x¯−x2−λn

(n−1)x¯+λn

nx¯−x2+λn

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detailed solution

Correct option is D

We have, x¯=x1+x2+…+xn−1+xnn⇒ nx¯=x1+x2…+xn−1+xnLet y→ be the new mean when x2 is replaced by λ Then, ⇒y¯=x1+x2+…+xn−x2+λn∴ y¯=nx¯−x2+λn

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Variate x	1	2	3	4	5
Frequency f of x	4	5	y	1	2

The mean of the series x1,x2,…,xn is x¯. If x2 is replaced by λ, then the new mean is

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Ready to Test Your Skills?

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The mean of the series $x_{1}, x_{2}, \dots, x_{n} is \bar{x}$ . If x₂ is replaced by $λ$ , then the new mean is