Question

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

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Answer 1

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
Clearly, reason (R) is true.
Using the relation given in reason (R), we have:
$$\begin{gathered} 2\mathrm{mean}=\left(3\times \mathrm{median}\right)-\mathrm{mode}=\left(3\times 150\right)-154=450-154=296 \\ \Rightarrow \mathrm{Mean}=148,\mathrm{}\mathrm{which}\mathrm{}\mathrm{is}\mathrm{}\mathrm{true}. \\ \therefore \mathrm{This}\mathrm{}\mathrm{assertion}\mathrm{}\left(\mathrm{A}\right)\mathrm{}\mathrm{and}\mathrm{}\mathrm{reason}\left(\mathrm{R}\right)\mathrm{}\mathrm{are}\mathrm{}\mathrm{both}\mathrm{}\mathrm{true}\mathrm{}\mathrm{and}\mathrm{}\mathrm{reason}\mathrm{}\left(\mathrm{R}\right)\mathrm{is}\mathrm{}\mathrm{the}\mathrm{}\mathrm{correct}\mathrm{}\mathrm{explanation}\mathrm{}\mathrm{of}\mathrm{}\mathrm{assertion}\mathrm{}\left(\mathrm{A}\right). \end{gathered}$$