Question

the mean of given data is 25. If each observations of the data is increased by 2, then find the new mean

Answer 1

Answer:

Step-by-step explanation:

x¯=∑xin=10

Mean of new observations

x¯′=∑(5xi+1)n=5∑(xi)+nn

=5∑(xi)n+1

=5⋅10+1

=51

Answer 2

Answer:

The new mean is 27.

Step-by-step explanation:

It is given that the mean of a data set is 25.

$Mean=\frac{\sum x}{n}$

where, x is observations and n is number of observations.

Let the mean of n observations is 25.

$\frac{x_1+x_2+...+x_n}{n}=25$

$x_1+x_2+...+x_n=25n$              .... (1)

It means the sum of n observations is 25n.

Each observations of the data is increased by 2, then the sum of n observations is

$\sum x_i=(x_1+2)+(x_2+2)+...+(x_n+2)$

$\sum x_i=(x_1+x_2+...+x_n)+2\times n$

Using (1) we get

$\sum x_i=25n+2n$

$\sum x_i=27n$

New mean of n observations is

$Mean=\frac{27n}{n}$

$Mean=27$

Therefore, the new mean is 27.