MCQ
Each question consists of two statements, namely, Assertion $(A)$ and Reason $(R).$ For selecting the correct answer: use the following code:
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
  • 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

Correct option: A.
Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
Reason $(R)$ is true.
Using the relation given in $(R),$ we have
Median $= 150$
Mode $= 154$
Mode $= 3$ Median $- 2$ Meen
Hence, mean $=\frac{3\text{Median}-\text{Mode}}{2}$
$=\frac{3(150)-154}{2}$
$=\frac{450-154}{2}$
$=\frac{296}{2}$
$=148$
Thus, Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$

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