Question

Assertion (A): If the value of each observation of a statistical data consisting of n terms is increased by 3 then the mean of the data increases by 3n.

Reason (R): The sum of the differences between individual observations and their mean is zero.

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 false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. Increasing each of the $$n$$ observations by 3 increases their total by $$3n$$, but the mean increases by $$\frac{3n}{n} = 3$$, not by $$3n$$.

Step 2 – Reason: R is true. The sum of the deviations of observations from their mean is zero.