Question

Mean of n numbers x₁, x₂, … x_n is m. If x_n is replaced by x, then new mean is ______.

पर्याय

• m - x_n + x

• `(nm-x_n+x)/n`

• `((n-1)m+x)/n`

• `(m-x_n+x)/n`

Answer 1

Mean of n numbers x₁, x₂, … x_n is m. If x_n is replaced by x, then new mean is `underline((nm-x_n+x)/n)`.

Explanation:-

`"Mean"=(x_1+x_2+x_3+...+x_n)/n=m`

⇒ x₁ + x₂ + ... + x_n = nm

⇒ x₁ + x₂ + ...x_n-1 + x_n = nm

⇒ x₁ + x₂ + ... + x_n-1 = nm - x_n

New sum = x₁ + x₂ + ... + x_n-1 + x

`"New Mean"=(x_1+x_2+x_3+...+x_n)/n`

`=(nm-x_n+x)/n`