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

Answer 1

Step-by-step explanation:

Step 1: Multiplied by 3

= x 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

${\large{\dag{\mathfrak{\red{\underline{\underline{Given :}}}}}}}$

• Observation of raw data = X
• Observation multiplied by = 3
• Observation is added to = 6
• Than divided by = 3
• Than reduced by = 6

________________________

${\large{\dag{\mathfrak{\blue{\underline{\underline{To Find:}}}}}}}$

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.

_______________________

${\large{\dag{\mathfrak{\orange{\underline{\underline{Solution :}}}}}}}$

Solving Starts :

Let the old mean be x :

Step 1 :-

Multiplied by 3

${\leadsto{\sf{X × 3 }}}$

${\purple{\bf{\red{\underline{3x}}}}}$

Step 2 :-

Added to 6

${\purple{\bf{\red{\underline{3x + 6}}}}}$

Step 3:-

Divided by 3

${\leadsto{\sf{(3x + 6) \div 3 }}}$

${\leadsto{\sf{[{\cancel 3} ( x + 2 ) ] \div {\cancel3}}}}$

${\purple{\bf{\red{\underline{x + 2}}}}}$

Step 4:-

Reduced by 6

${\leadsto{\sf{(X + 2 ) - 6}}}$

${\purple{\bf{\red{\underline{x - 4}}}}}$

So,

${\purple{\twoheadrightarrow{\pink{\boxed{\orange{\bf{New \: Mean = X - 4}}}}}}}$

Hence,

Original mean is reduced by 4 new mean will also be reduced by 4.

${\purple{\underline{\blue{\underline{\red{\boxed{\bf{C \: is \: correct.}}}}}}}}$

_______________________