Ten observations 6, 14, 15, 17, x+1, 2x-13, 3 | vedclass

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(A) The given observations are $6, 14, 15, 17, x+1, 2x-13, 30, 32, 34, 43$,which are already in ascending order.Here,the number of observations $n = 1

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(A) The given observations are $6, 14, 15, 17, x+1, 2x-13, 30, 32, 34, 43$,which are already in ascending order.Here,the number of observations $n = 10$,which is an even number.For an even number of observations,the median is the average of the $(\frac{n}{2})^{th}$ term and the $(\frac{n}{2} + 1)^{th}$ term.Median $= \frac{5^{th} 	ext{ term} + 6^{th} 	ext{ term}}{2}$.Given the $5^{th}$ term is $(x+1)$ and the $6^{th}$ term is $(2x-13)$,we have:Median $= \frac{(x+1) + (2x-13)}{2} = \frac{3x-12}{2}$.Given that the median is $24$,we set up the equation:$\frac{3x-12}{2} = 24$.$3x - 12 = 48$.$3x = 48 + 12 = 60$.$x = \frac{60}{3} = 20$.Thus,the value of $x$ is $20$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$5$	$7$	$12$	$9$	$13$	$5$

Ten observations $6, 14, 15, 17, x+1, 2x-13, 30, 32, 34, 43$ are written in an ascending order. The median of the data is $24$. Find the value of $x$.

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