The S.D. of a variate x is sigma. The S.D. of | vedclass

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

Question

(b) Let $y = \frac{{ax + b}}{c}$ i.e., $y = \frac{a}{c}x + \frac{b}{c}$

i.e., $y = Ax + B$, where $A = \frac{a}{c}$,$B = \frac{b}{c}$

 $\ba

Vedclass · Accepted Answer

$\left| {\frac{a}{c}} \right|\,\sigma $

Vedclass · Answer

(b) Let $y = \frac{{ax + b}}{c}$ i.e., $y = \frac{a}{c}x + \frac{b}{c}$

i.e., $y = Ax + B$, where $A = \frac{a}{c}$,$B = \frac{b}{c}$

 $\bar y = A\bar x + B$

 $y - \bar y = A(x - \bar x)$ ==> ${(y - \bar y)^2} = {A^2}{(x - \bar x)^2}$

==> $\sum {(y - \bar y)^2} = {A^2}\sum {(x - \bar x)^2}$

==> $n.\sigma _y^2 = {A^2}.n\sigma _x^2$ ==> $\sigma _y^2 = {A^2}\sigma _x^2$

==> ${\sigma _y} = \,|A|{\sigma _x}$ ==> ${\sigma _y} = \,\left| {\frac{a}{c}} \right|{\sigma _x}$

Thus, new $S.D$. $ = \left| {\frac{a}{c}} \right|\,\sigma $.

$X_i$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency $f_i$	$3$	$6$	$16$	$\alpha$	$9$	$5$	$6$

The $S.D.$ of a variate $x$ is $\sigma$. The $S.D.$ of the variate $\frac{{ax + b}}{c}$ where $a, b, c$ are constant, is

Similar Questions

Mean and standard deviation of 100 observations were found to be 40 and 10 , respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

If the variance of the frequency distribution is $3$ then $\alpha$ is ......

$X_i$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

Frequency $f_i$ $3$ $6$ $16$ $\alpha$ $9$ $5$ $6$

Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a _1, a _2, a _3, \ldots ., a _{100}$ is $25$. Then $S$ is

The frequency distribution:

$\begin{array}{|l|l|l|l|l|l|l|} \hline X & 2 & 3 & 4 & 5 & 6 & 7 \\ f & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}$

Find the standard deviation.

For two data sets, each of size $5$, the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$, respectively. The variance of the combined data set is