Question

help with stats. :o

Answer 1

\[\sigma^2= \overline{x^2}-\overline{x}^2\]

Answer 2

the over bar means take the mean (or average) .
the variance is the mean of the squares minus the square of the mean

Answer 3

ive never had much practice with this version, but the google gives me
\[\frac{n(\sum x^2)-(\sum x)^2}{n(n-1)}\]

Answer 4

http://www.saddleback.edu/faculty/pquigley/math10/shortcut.pdf

ive always used the:\[\frac{\sum (x-\bar x)^2}{n-1}\]

but they dont really give that information in this question

Answer 5

using n rather than n-1 (difference between sample stats and population stats)
\[ \frac{\sum (x-\bar x)^2}{n}= \frac{\sum{x^2}}{n}-2 \bar x \frac{\sum{x}}{n}+\frac{\sum{(\bar x)^2}}{n}\]
the first term is \( \bar {x^2} \)
noting that the square of the mean is constant, that last term is
\[ (\bar x)^2 \cdot \frac{n}{n} \]
and the expression simplifies to
\[ \overline{x^2} - \overline{x}^2 \]

Answer 6

and the middle term is \( -2 \overline{x}^2 \)