Question

Assertion : If the median of the given data 26, 29, 42, 53, x, x + 2, 70, 75, 82, 93, is 65 then the value of x is 64.
Reason : When the number of observations(n) is odd the median is the value of the ${\left(\frac{n+1}{2}\right)}^{th}$ observation.
Which of the following is correct.

• A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
• B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
• C. If Assertion is correct but Reason is incorrect.
• D. If Assertion is incorrect but Reason is correct.

Answer 1

The correct option is B If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

Assertion : Given no. observation is 10 (even)
Median $=\frac{x+(x+2)}{2}=\frac{2x+2}{2}=x+1$
$65=x+1\Rightarrow x=64$
Reason is also true. But Reason is not correct explanation of Assertion.