Solve the variance problem below - statistics

[chwala]

Homework Statement

see attached

Relevant Equations

variance

The question is below:

below is my own working;

the mark scheme for the question is below here;

i am seeking for any other approach that may be there...am now trying to refresh on stats...bingo!

 

[Mark44]

Homework Statement:: see attached
Relevant Equations:: variance

The question is below:

View attachment 291394

below is my own working;
View attachment 291395the mark scheme for the question is below here;
View attachment 291396

i am seeking for any other approach that may be there...am now trying to refresh on stats...bingo!

Here's a quicker way:
$\sum (x - \bar x)^2 = \sum x^2 - N \cdot \bar x^2$

Proof:
$\sum (x - \bar x)^2 = \sum(x^2 - 2x\cdot \bar x + \bar x^2)$
$= \sum x^2 - 2\cdot \bar x \sum x + \sum \bar x^2 = \sum x^2 - 2\bar x \cdot N \cdot \bar x + N \bar x^2 = \sum x^2 - N \cdot \bar x^2$
All summations are from n = 1 to N.
In the proof above, I'm using the fact that $\sum x = N \bar x$

 

[chwala]

Is the proof missing something...I will counter check it later...

 

[chwala]

I just had a look at your proof...thanks Mark...I wasn't certain on the last part of your equation involving the mean. Its now clear to me from my study (shown below). Bingo!

 

[Mark44]

I just had a look at your proof...thanks Mark...I wasn't certain on the last part of your equation involving the mean. Its now clear to me from my study. Bingo!

Yes, that's it. I've edited my post to change 'n' to 'N', which I hope makes it clearer.