Assertion (A): Median of first eleven prime numbers is 13. Reason (R): Median of a grouped frequency distribution is give

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Solution

Q.
Assertion (A): Median of first eleven prime numbers is 13.

Reason (R): Median of a grouped frequency distribution is given by $M e d i a n = l + (\frac{\frac{n}{2} - c f}{f}) \times h, w h e r e (l) =$ ower limit of the median class, cf = cumulative frequency of the class preceding the median class, f = frequency of the median class, h = class width and n= total frequency.

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

2 Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A)

3 Assertion (A) is true but Reason (R) is false.

4 Assertion (A) is false but Reason (R) is true.

Ans.
(2)

First eleven prime numbers are $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31$

$H e r e, (n = 11) (o d d)$

$∴ Median = {(\frac{n + 1}{2})}^{th} observation = {(\frac{11 + 1}{2})}^{th} observation$

$= 6^{th} observation = 13 A s s e r t i o n i s t r u e .$

$M e d i a n o f a g r o u p e d f r e q u e n c y d i s t r i b u t i o n i s g i v e n b y$

$Median = l + (\frac{\frac{n}{2} - c f}{f}) \times h$

Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

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