Question

Assertion: (A) In a graphical representation, if p times the distance between the Median and Mean is thrice the distance between Mode and Mean, then the value of p is 9.
Reason: (R) Mode= 3 Median - 2 Mean
Which of the following is true?

• A. (A) and (R) are true and (R) is the correct explanation of (A)
• B. (A) is false and (R) is the correct explanation of (A)
• C. (A) is true and (R) is false
• D. Both (A) and (R) are false

Answer 1

The correct option is A

(A) and (R) are true and (R) is the correct explanation of (A)

Assertion (A)
$\because$ p(Median-Mean) = 3 (Mode-Mean) [given]
We know that,
Mode = 3 Median - 2 Mean
p(Median-Mean)= 3 (3 Median - 2 Mean - Mean)
$\Rightarrow$ p(Median-Mean)= 3 (3 Median - 3 Mean)
$\Rightarrow$ p(Median-Mean)= 3$\times$ 3 (Median - Mean)
$\Rightarrow$ p(Median-Mean)= 9 (Median-Mean)
$\Rightarrow$p = 9
$\therefore$Reason (R) is True.