Assertion (A): If in a moderately skewed distribution the value of mode and mean are 4λ and 7λ respectively, then value of median is 5λ Reason (R ): For a moderately skewed distribution Mode = 3 Median - 2 Mean

Question

Assertion (A): If in a moderately skewed distribution the value of mode and mean are 4λ and 7λ respectively, then value of median is 5λ Reason (R ): For a moderately skewed distribution Mode = 3 Median - 2 Mean (A) Both (A) (R) are individually true (R) is correct explanation of (A). (B) Both (A) (R ) are individually true but (R) is not the correct (proper) explanation of (A) (C) (A) is true (R) is false (D) (A) is false (R) is true

Tardigrade Admin · Accepted Answer

∵ Mode = 3 Median - 2 Mean ⇒ 4 λ =3 Median -2(7 λ) ⇒ Median =(4 λ +14λ/3)=6λ ⇒ Assertion (A) is false but Reason (R) is true

Q. Assertion (A) : If in a moderately skewed distribution the value of mode and mean are $4 λ$ and $7 λ$ respectively, then value of median is $5 λ$
Reason (R ) : For a moderately skewed distribution Mode = 3 Median - 2 Mean

Both (A) & (R) are individually true & (R) is correct explanation of (A).

Both (A) & (R ) are individually true but (R) is not the correct (proper) explanation of (A)

(A) is true (R) is false

(A) is false (R) is true

$∵$ Mode = 3 Median - 2 Mean
$\Rightarrow 4 λ = 3$ Median $- 2 (7 λ)$
$\Rightarrow$ Median $= \frac{4 λ + 14 λ}{3} = 6 λ$
$\Rightarrow$ Assertion (A) is false but Reason (R) is true

Q. Assertion (A) : If in a moderately skewed distribution the value of mode and mean are 4λ and 7λ respectively, then value of median is 5λ Reason (R ) : For a moderately skewed distribution Mode = 3 Median - 2 Mean