Linear function of a variable

[chengeto]

Guys l have the following data:

I calculated the mean which is 25 and l also calculated the standard deviation which is 3.74. Now they want me to show that :

if \(\displaystyle y=ax+b\) then \(\displaystyle \bar{y}=a\bar{x}+b\) and \(\displaystyle s_{y}= \left| a\right|s_{x}\)

So guys how do l prove this ?

 

[Deleted member 4993]

Guys l have the following data:

I calculated the mean which is 25 and l also calculated the standard deviation which is 3.74. Now they want me to show that :

if \(\displaystyle y=ax+b\) then \(\displaystyle \bar{y}=a\bar{x}+b\) and \(\displaystyle s_{y}= \left| a\right|s_{x}\)

So guys how do l prove this ?

Those are general theorem - irrespective of data:

\(\displaystyle y_1 \, = \, a * x_1 \, + \, b\)

\(\displaystyle y_2 \, = \, a * x_2 \, + \, b\)

\(\displaystyle y_3 \, = \, a * x_3 \, + \, b\)
.
.
.
\(\displaystyle y_n \, = \, a * x_n \, + \, b\)
__________________________________ adding together

\(\displaystyle \sum_{i=1}^n y_i \, = \, a * \sum_{i=1}^n x_i \, + \, n * b\)

\(\displaystyle \frac{\sum_{i=1}^n y_i }{n}\, = \, a * \frac{\sum_{i=1}^n x_i}{n} \, + \, b\)

and so on ....

 

[chengeto]

Guys l have the following data:

I calculated the mean which is 25 and l also calculated the standard deviation which is 3.74. Now they want me to show that :

if \(\displaystyle y=ax+b\) then \(\displaystyle \bar{y}=a\bar{x}+b\) and \(\displaystyle s_{y}= \left| a\right|s_{x}\)

So guys how do l prove this ?

Those are general theorem - irrespective of data:

\(\displaystyle y_1 \, = \, a * x_1 \, + \, b\)

\(\displaystyle y_2 \, = \, a * x_2 \, + \, b\)

\(\displaystyle y_3 \, = \, a * x_3 \, + \, b\)
.
.
.
\(\displaystyle y_n \, = \, a * x_n \, + \, b\)
__________________________________ adding together

\(\displaystyle \sum_{i=1}^n y_i \, = \, a * \sum_{i=1}^n x_i \, + \, n * b\)

\(\displaystyle \frac{\sum_{i=1}^n y_i }{n}\, = \, a * \frac{\sum_{i=1}^n x_i}{n} \, + \, b\)

and so on ....

\(\displaystyle s^2_{y}=(a^2)\cdot(s^2_{x})\)
\(\displaystyle \sqrt{(s^2_{y})}=\sqrt{(a^2)\cdot(s^2_{x})\)
\(\displaystyle s_{y}= \left| a\right|s_{x}\)

Is this correct ?