Find the median of the sequence ^{2n}C_0, ^{2 | vedclass

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

Question

(B) The sequence is $^{2n}C_0, ^{2n}C_1, ^{2n}C_2, \dots, ^{2n}C_n$.The number of terms in the sequence is $n + 1$.Since $n$ is even,$n + 1$ is odd.Th

Vedclass · Accepted Answer

$^{2n}C_{\frac{n}{2}}$

Vedclass · Answer

(B) The sequence is $^{2n}C_0, ^{2n}C_1, ^{2n}C_2, \dots, ^{2n}C_n$.The number of terms in the sequence is $n + 1$.Since $n$ is even,$n + 1$ is odd.The median of a sequence with an odd number of terms $N$ is the term at position $\frac{N+1}{2}$.Here,$N = n + 1$,so the median is the term at position $\frac{(n+1)+1}{2} = \frac{n+2}{2} = \frac{n}{2} + 1$.The term at position $\frac{n}{2} + 1$ in the sequence $^{2n}C_0, ^{2n}C_1, \dots, ^{2n}C_n$ is $^{2n}C_{n/2}$.

$x_i$	$3$	$6$	$9$	$12$
$f_i$	$1$	$2$	$3$	$4$

Find the median of the sequence $^{2n}C_0, ^{2n}C_1, ^{2n}C_2, \dots, ^{2n}C_n$ (where $n$ is even).

Similar Questions

$x_1, x_2, \dots, x_{34}$ 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 $x_1, x_2, \dots, x_{34}$.

The mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha$ $(\alpha \neq 0)$ and then increased by $10$,what is the mean of the new set?

Which of the following averages is most affected by extreme observations?

If a variable takes the discrete values $\alpha - 4, \alpha - \frac{7}{2}, \alpha - \frac{5}{2}, \alpha - 3, \alpha - 2, \alpha + \frac{1}{2}, \alpha - \frac{1}{2}, \alpha + 5$ (where $\alpha > 0$),then the median is:

Find the mean of the following frequency distribution:

$x_i$ $3$ $6$ $9$ $12$

$f_i$ $1$ $2$ $3$ $4$

Vedclass Test Series

Exam Paper Generator

Online Exam Module