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