Question

Assertion (A)	Reason (R)
If the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148.	Mean, median and mode of a frequency distribution are related as: mode = 3 median – 2 mean.

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

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

Explanation:

Reason (R) is clearly true.

Using the relation given in Reason (R), we have

2 mean = (3 median) – (mode)

= (3 × 150) – (154) 

= 450 – 154

= 296

∴ Mean = 148, which is true.

Thus, Assertion (A) and Reason (R) are both true and Reason (R) is the correct explanation of Assertion (A).