Consider three observations a, b, and c such | vedclass

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

Question

(C) The mean of $a, b, c$ is $\bar{x} = \frac{a+b+c}{3}$.Since $b = a + c$,we have $\bar{x} = \frac{b+b}{3} = \frac{2b}{3}$.The standard deviation of

Vedclass · Accepted Answer

$b^2 = 3(a^2 + c^2) - 9d^2$

Vedclass · Answer

(C) The mean of $a, b, c$ is $\bar{x} = \frac{a+b+c}{3}$.Since $b = a + c$,we have $\bar{x} = \frac{b+b}{3} = \frac{2b}{3}$.The standard deviation of $a+2, b+2, c+2$ is the same as the standard deviation of $a, b, c$,which is $d$.Thus,$d^2 = \frac{a^2+b^2+c^2}{3} - (\bar{x})^2$.$d^2 = \frac{a^2+b^2+c^2}{3} - \left(\frac{2b}{3}\right)^2$.$d^2 = \frac{a^2+b^2+c^2}{3} - \frac{4b^2}{9}$.$d^2 = \frac{3(a^2+b^2+c^2) - 4b^2}{9}$.$9d^2 = 3(a^2+c^2+b^2) - 4b^2$.$9d^2 = 3(a^2+c^2) + 3b^2 - 4b^2$.$9d^2 = 3(a^2+c^2) - b^2$.Therefore,$b^2 = 3(a^2+c^2) - 9d^2$.

Consider three observations $a, b,$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following holds true?

Similar Questions

The variance of the observations $8, 12, 13, 15, 22$ is:

If the variance of $x_1, x_2, \ldots, x_n$ is $\sigma_x^2$,then the variance of $\lambda x_1, \lambda x_2, \ldots, \lambda x_n$ (where $\lambda \neq 0$) is:

Let $n$ observations $x_1, x_2, ....., x_n$ be such that $\sum {x_i}^2 = 400$ and $\sum x_i = 80$. Then,which of the following is a possible value for $n$?

If the mean of $10$ observations is $50$ and the sum of the squares of the deviations of the observations from the mean is $250$,then the coefficient of variation of those observations is

$A$ data consists of $20$ observations $x_1, x_2, ..., x_{20}$. If $\sum_{i=1}^{20} (x_i + 5)^2 = 2500$ and $\sum_{i=1}^{20} (x_i - 5)^2 = 100$, then the ratio of mean to standard deviation of this data is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module