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)
p = 9 [by comparing]
Reason (R) is True.