Question

Mean of 20 observation is 25. If its observation is divided by 3. Find the new mean.​

Answer 1

GIVEN

The Mean of 20 Observation = 25

New Observations are divided by 3

TO FIND

The New Mean

SOLUTION

Let the observations are A1, A2, A3, A4, ......, A20

The Mean is 20

(A1+A2+A3+.....+A20)/20 = 25

=>(A1+A2+A3+.....+A20) = 500

Now new mean observations are divided by 3 from each,

(A1/3+A2/3+A3/3+.....+A20/3) = 500

=> 1/3 (A1+A2+A3+.....+A20) = 500

=> (A1+A2+A3+.....+A20) = 1500 ...eq.01

We know that

Mean =

Sum of All Observations / No. of Obseravations

New Mean (A1+A2+A3+.....+A20)/20

= 1500/20. (from eq.01)

= 75.

Hence the New Mean is 75. (ANS)

Answer 2

AnswEr:

$\boxed{ \bold {\underline{new \: mean \: is \: <strong>7</strong><strong>5</strong>}}}$

Step-by-step explanation:

Given :

• Mean of 20 observation is 25 and
• each observation is divided by 3

To Find:

• The new mean = ?

Solution:

We know that ,

$\sf{mean \: = \frac{sum \: of \: all \: observations}{total \: number \: of \: observation}}$

$25 = \sf \: \frac{sum}{20} \\ \\ \sf \: sum \: = 20 \times 25 \\ \\ \sf \: sum \: = \: 500$

According to question ,

Given that , all observations re divided by 3

So ,

= 500 × 3 = 1500

= Sum of all observations/ 3

= 1500/ 3

= Hence , the new mean is 75