If the mean of the set of numbers `x_1,x_2, x_3, ..., x_n` is `barx,` then the mean of the numbers `x_i+2i, 1 lt= i lt= n` is

Question

If the mean of the set of numbers `x_1,x_2, x_3, ..., x_n` is `barx,` then the mean of the numbers `x_i+2i, 1 lt= i lt= n` is

If the mean of the set of numbers `x_1,x_2, x_3, ..., x_n` is `barx,` then the mean of the numbers `x_i+2i, 1 lt= i lt= n` is
A. `overline (x)+2n`
B. `overline(x)+n+1`
C. `overline(x)+2`
D. `overline(x)+n`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - B
We know that `overline(x)=(underset(i=1)overset(n)(sum x_(i)))/(n)`
`implies underset(i=1)overset(n)(sum x_(i))=noverline(x)`
`therefore (underset(i=1)overset(n)(sum(x_(i)+2i)))/(n)=(underset(i=1)overset(n)(sum x_(i)+2)underset(i=1)overset(n)(sum i))/(n)=(noverline(x)+2(1+2+..n))/(n)`
`=(noverline(x)+2(n(n+1))/(2))/(n)=overline(x)+(n+1)`