Question

Assertion : The median of the following observation 0, 1, 2, 3, x, x+2, 8, 9, 11, 12 which arranged in ascending order is 63, then the value of x is 62.
Reason : Median of n even observations is $\frac{{\left(\frac{n}{2}\right)}^{th}term+{(\frac{n}{2}+1)}^{th}term}{2}$
Which of the following is correct.

• A. If both assertion and reason are true and reason is the correct explanation of assertion.
• B. If both assertion and reason are true but reason is not correct explanation of assertion.
• C. If assertion is true but reason is false
• D. If assertion is false but reason is true.

Answer 1

The correct option is A If both assertion and reason are true and reason is the correct explanation of assertion.

Number of terms = 10 (even)
Median of n even number of terms
$=\frac{{\left(\frac{n}{2}\right)}^{th}term+{(\frac{n}{2}+1)}^{th}term}{2}$
$=\frac{5^{th}term+6^{th}term}{2}=\frac{x+x+2}{2}=63$
$\Rightarrow 2x+2=126$
$\Rightarrow x=62$