MCQ
Each question consists of two statements, namely, Assertion $(A)$ and Reason $(R)$. For selecting the correct answer: use the following code:
Assertion $(A)$
Consider the following frequency distribution:
Class interval
$3-6$ $6-9$ $9-12$ $12-15$ $15-18$ $18-21$
Frequency
$2$ $5$ $21$ $23$ $10$ $12$
The mode of the above data is $12.4.$
Reason $(R)$
The value of the variable which occurs most often is the mode.
  • A
    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 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: B.
Both Assertion $(A)$ and Reason $(R)$ are true but Reason $(R)$ is a not a correct explanation of Assertion $(A).$
Reason $(R)$ is true.
Maxximum frequency $= 23$
Hence, modakl class is $12-15$
Now, mode $=\text{x}_\text{k}+\text{h}\Big\{\frac{(\text{f}_\text{k}-\text{f}_{\text{k}-1})}{(2\text{f}_\text{k}-\text{f}_{\text{k}-1}-\text{f}_{\text{k}+1})}\Big\}$
$=12+3\Big\{\frac{(23-21)}{(2(23)-21-10)}\Big\}$
$=12+3\times\frac{2}{15}$
$=12+0.4$
$=12.4$

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