Assertion (A): Median of first 9 terms of Fibonacci sequence is 3. Reason (R): Median of a grouped frequency distribution is given by

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Solution

Q.
Assertion (A): Median of first 9 terms of Fibonacci sequence is 3.

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

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.
(3)

$F i b o n a c c i s e q u e n c e : 0, 1, 1, 2, 3, 5, 8, 13, 21 H e r e, n = 9, w h i c h i s o d d . ∴ Median = {(\frac{n + 1}{2})}^{th} observation = 5^{th} observation = 3 ∴ Assertion (A) is true. M e d i a n o f g r o u p e d f r e q u e n c y d i s t r i b u t i o n i s g i v e n b y Median = l + (\frac{\frac{n}{2} - c f}{f}) \times h ∴ Reason (R) is false. T h u s, A s s e r t i o n (A) i s t r u e a n d R e a s o n (R) i s f a l s e .$

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