The average of n numbers $$x1$$,$$x2$$,$$x3$$,…,xn is M. If xn is replaced by x', then new average is

Correct option is 2nM−xn+x′n

Questions

The average of n numbers $x_{1}, x_{2}, x_{3}, \dots, x_{n}$ is M. If $x_{n}$ is replaced by x', then new average is

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M−xn+x′

nM−xn+x′n

(n−1)M+x′n

M−xn+x′n

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detailed solution

Correct option is B

M=x1+x2+x3……xnn⇒ nM=x1+x2+x3+…+xn−1+xn⇒ nM−xn=x1+x2+x3+…+xn−1⇒ nM−xn+x′=x1+x2+x3+…+xn−1+x′⇒ nM−xn+x′n=x1+x2+x3+…+xn−1+x′n∴ New average=nM−xn+x′n

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

The average of n numbers x1,x2,x3,…,xn is M. If xn is replaced by x', then new average is

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The average of n numbers $x_{1}, x_{2}, x_{3}, \dots, x_{n}$ is M. If $x_{n}$ is replaced by x', then new average is