x_1, x_2, dots, x_{34} are numbers such that | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The sequence has $34$ terms. The median is the average of the $17^{	ext{th}}$ and $18^{	ext{th}}$ terms.Given $x_1 = x_2 = \dots = x_{10} = 150$

Vedclass · Accepted Answer

$135$

Vedclass · Answer

(C) The sequence has $34$ terms. The median is the average of the $17^{	ext{th}}$ and $18^{	ext{th}}$ terms.Given $x_1 = x_2 = \dots = x_{10} = 150$.For $i \ge 10$,the sequence follows $x_{i+1} = x_i - 2$,which is an arithmetic progression with first term $a = x_{10} = 150$ and common difference $d = -2$.The $n^{	ext{th}}$ term of this progression (starting from $i=10$) is $x_{10+k} = 150 + k(-2)$.For the $17^{	ext{th}}$ term,$10+k = 17 \implies k = 7$,so $x_{17} = 150 + 7(-2) = 150 - 14 = 136$.For the $18^{	ext{th}}$ term,$10+k = 18 \implies k = 8$,so $x_{18} = 150 + 8(-2) = 150 - 16 = 134$.The median is $\frac{x_{17} + x_{18}}{2} = \frac{136 + 134}{2} = \frac{270}{2} = 135$.

$x_i$	$5$	$8$	$11$	$14$	$17$
$f_i$	$4$	$5$	$6$	$10$	$20$

$x_1, x_2, \dots, x_{34}$ are numbers such that $x_i = 150$ for all $i \in \{1, 2, \dots, 10\}$ and $x_{i+1} - x_i = -2$ for all $i \in \{10, 11, \dots, 33\}$. Find the median of $x_1, x_2, \dots, x_{34}$.

Similar Questions

Which of the following,in the case of discrete data,is not equal to the median?

Find the arithmetic mean of the following frequency distribution.

$x_i$ $5$ $8$ $11$ $14$ $17$

$f_i$ $4$ $5$ $6$ $10$ $20$

If the mean of $n$ observations $1^2, 2^2, 3^2, \dots, n^2$ is $\frac{46n}{11}$,then what is the value of $n$?

The median of a set of $9$ distinct observations is $20.5$. If the four largest observations of the set are increased by $2$,what will be the median of the new set?

The $A.M.$ of a $50$ set of numbers is $38$. If two numbers of the set,namely $55$ and $45$,are discarded,the $A.M.$ of the remaining set of numbers is

Vedclass Test Series

Exam Paper Generator

Online Exam Module