Question

Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6. Which of the following statement is true?

(A) the new mean is equal to the original mean

(B) the new mean is 4 more than the original mean

(C) the new mean is 4 less than the original mean

(D) the new mean is 2 more than the original mean

An Explanation would be appreciated! :)

Answer 1

$<b><font face=copper black size=4 colour=purple>$Let,

Each observation = x

A/q

Step 1 : Multiplied by 3

= x × 3 = 3x

Step 2 : 6 is added

= 3x + 6

Step 3 : Divided by 3

= ( 3x + 6 ) / 3

= [ 3 ( x + 2 ) ] / 3

= x + 2

Step 4 : Reduced by 6

= x + 2 - 6

= x - 4

This shows that each observation is decreased by 4.

So, there will be decrease in the new mean also.

Hence,

Option C) is correct.

^^"

Answer 2

Answer:

Step-by-step explanation:

Step 1 : Multiplied by 3

= x × 3 = 3x

Step 2 : 6 is added

= 3x + 6

Step 3 : Divided by 3

= ( 3x + 6 ) / 3

= [ 3 ( x + 2 ) ] / 3

= x + 2

Step 4 : Reduced by 6

= x + 2 - 6

= x - 4

This shows that each observation is decreased by 4.

So, there will be decrease in the new mean also.

Hence,

Option C) is correct.

Read more on Brainly.in - https://brainly.in/question/7130300#readmore