Question

The mean of a given set of observation is 30. If each observation is increased by 3, find the mean of the new observation.

Answer 1

SOLUTION

GIVEN

• The mean of a given set of observation is 30.

• Each observation is increased by 3

TO DETERMINE

The mean of the new observation

EVALUATION

Let there are n observations say

$\sf{x_1, x_2,.., x_n}$

Now mean is 30

So by the given condition

$\displaystyle \sf{ \frac{x_1 + x_2 + .. + x_n}{n} = 30}$

Now each observation is increased by 3

So the new observations are

$\sf{(x_1 + 3),( x_2 + 3),.., (x_n + 3)}$

So the required mean

$\displaystyle \sf{ = \frac{(x_1 + 3) + (x_2 +3) .. +( x_n + 3)}{n} }$

$\displaystyle \sf{ = \frac{x_1 + x_2 + .. + x_n + 3n}{n} }$

$\displaystyle \sf{ = \frac{x_1 + x_2 + .. + x_n }{n} + \frac{3n}{n} }$

$\displaystyle \sf{ = 30 + 3 }$

$= 33$

FINAL ANSWER

Hence the required mean of the new observation = 33

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. 6 years ago, Mahima mother age was 3 times as old as Mahima. After 5 years, she will be twice as old as Mahima. Present ...

https://brainly.in/question/36116267

2. 5 years ago, Bharti's mother was 3 times as. old as. Bharti . After 6 years she will be twice as old as Bharti Present...

https://brainly.in/question/36004926