Question

Assertion (A): If a 'less than' type and 'more than' type cumulative frequency curves of a grouped data intersect at (9, 12) then the median of the data is 9.

Reason (R): The ordinate of the point of intersection of 'less than' type and 'more than' type cumulative frequency curves of a grouped data gives its median.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. The median is given by the abscissa (the x-coordinate) of the intersection of the two ogives. For the intersection point $$(9,12)$$, the median is 9.

Step 2 – Reason: R is false. It is the abscissa, not the ordinate, of the intersection point that gives the median.