Question

The mean of a data is 9 if each obsevation by multiplied by 3 and then 1
is added to each result, find the
mean of the new observations so obtained​

Answer 1

Answer:

Step-by-step explanation:

Let the number of observations be x

Initially, Sum = 9*x

now, Sum=9*(3*x)+1*x = 28x

Hence, mean = 28x/x = 28

Answer 2

Answer:-

Mean = 28

$\rule{100}2$

Explanation-

The mean of a data is 9.

Means, sum of all observations is 9.

Let there are 'M' number of observations.

$\Rightarrow\:\sf{x_1++x_2+x_3+....+x_9\:=\:9}$

For 'M' number of observations.

$\Rightarrow\:\sf{x_1+x_2+x_3+.....+x_M\:=\:9M}$

If each observation is multiplied by 3.

Then,

$\Rightarrow\:\sf{3x_1+3x_2+3x_3+....+3x_M}$

Take 3 as common

$\Rightarrow\:\sf{3(x_1+x_2+x_3+.....+x_M)}$

From above,

$\Rightarrow\:\sf{3(9M)}$

$\Rightarrow\:\sf{27M}$

If 1 is added to each result. Then,

$\Rightarrow\:\sf{27M\:+\:(1+1+...+M \:times)}$

$\Rightarrow\:\sf{27M\:+\:M}$

$\Rightarrow\:\sf{28M}$

Now, we have

Sum of observations = 28M

And total number of observations = M

Mean = Sum of all observations/Total number of observations

Substitute the known values

⇒ 28M/M

⇒ 28

$\rule{200}2$

In short

Total number of observations = 9

Each observation is multiplied by 3

⇒ 9 × 3

⇒ 27

Then, 1 is added to each observation

⇒ 27 + 1

⇒ 28