Question

Mean of n numbers x1,x2,x3,......,xn is m.If xn is replaced by x,then find the new mean

Answer 1

hi Gaurav,

sum = n*m

new sum = nm - xn + x

new mean = (nm - xn + x )/n

Hope it helped.
Please let me know if any further doubts.

Answer 2

Answer:

$\frac{mn - x_n +x}{n}$

Step-by-step explanation:

Given : Mean of n numbers $x_1,x_2,x_3,......,x_n$ is m.

To Find :.If $x_n$ is replaced by x,then find the new mean

Solution :

Mean of n numbers $x_1,x_2,x_3,......,x_n$ is m.

$Average = \frac{\text{Sum of all observations}}{\text{No. of observations}}$

$m = \frac{x_1+x_2+x_3+......+x_n}{n}$

$mn = x_1+x_2+x_3+......+x_n$

So, new sum = $mn - x_n +x$

$Average = \frac{\text{Sum of all observations}}{\text{No. of observations}}$

$Average = \frac{mn - x_n +x}{n}$

Hence the new mean is $\frac{mn - x_n +x}{n}$