# Thread: mean and standard deviation....

1. ## mean and standard deviation....

hi all,
i have a problem with this question....

A summary of 24 observations of x gave the following information:
$\displaystyle \sum(x-a)=-73.2$ and $\displaystyle \sum(x-a)^2=2115$
the mean of these value of x is 8.95
a) find the value of the constant a.
b) find the standard deviation of the value of x.

in this following case, that
$\displaystyle \sum(x-a)=\sum (x)-\sum (a)$ true??

thanks....

2. Originally Posted by pencil09
hi all,
i have a problem with this question....

A summary of 24 observations of x gave the following information:
$\displaystyle \sum(x-a)=-73.2$ and $\displaystyle \sum(x-a)^2=2115$
the mean of these value of x is 8.95
a) find the value of the constant a.
b) find the standard deviation of the value of x.

in this following case, that
$\displaystyle \sum(x-a)=\sum (x)-\sum (a)$ true??

thanks....
$\displaystyle \sum(x-a)=\sum (x)-\sum (a)$ true?? duno if that's true or not but here is how you do it:

let $\displaystyle y=x-a$

Then $\displaystyle \sum y = -73.2 \Rightarrow \overline{y}=\frac{\sum y}{n}=\frac{-73.2}{24}=-3.05$

Now $\displaystyle x=y+a \Rightarrow \overline{x} = \overline{y} + a = 8.95$ rearrange to find a. where $\displaystyle \overline{x} = 8.95$ and $\displaystyle \overline{y}=-3.05$

b) $\displaystyle \sum y^2=2115 \Rightarrow sdy= \sqrt{\frac{\sum y^2}{n} - \overline{y^2}} = \sqrt{\frac{2115}{24} - 3.05^2} = 8.87 (3s.f.)$

$\displaystyle sdx=1 * sdy = 8.87 (3s.f.)$

3. Originally Posted by BabyMilo
$\displaystyle \sum(x-a)=\sum (x)-\sum (a)$ true?? duno if that's true or not but here is how you do it:

let $\displaystyle y=x-a$

Then $\displaystyle \sum y = -73.2 \Rightarrow \overline{y}=\frac{\sum y}{n}=\frac{-73.2}{24}=-3.05$

Now $\displaystyle x=y+a \Rightarrow \overline{x} = \overline{y} + a = 8.95$ rearrange to find a. where $\displaystyle \overline{x} = 8.95$ and $\displaystyle \overline{y}=-3.05$

b) $\displaystyle \sum y^2=2115 \Rightarrow sdy= \sqrt{\frac{\sum y^2}{n} - \overline{y^2}} = \sqrt{\frac{2115}{24} - 3.05^2} = 8.87 (3s.f.)$

$\displaystyle sdx=1 * sdy = 8.87 (3s.f.)$

4. Originally Posted by pencil09
hi all,
i have a problem with this question....

A summary of 24 observations of x gave the following information:
$\displaystyle \sum(x-a)=-73.2$ and $\displaystyle \sum(x-a)^2=2115$
the mean of these value of x is 8.95
a) find the value of the constant a.
b) find the standard deviation of the value of x.

in this following case, that
$\displaystyle \sum(x-a)=\sum (x)-\sum (a)$ true??

thanks....