Variability!

The variance, written as s^2 or sigma^2, is the mean of the squares of the deviations from x bar.
The standard deviation, denoted s or sigma, is the positive square root of the variance.

s=sample
sigma=population
the strange E=sum
x^i=numbers
n=how many numbers you have
x bar=average(mean)
s=sample standard deviation

The bigger the deviation, the more the numbers are spread out.
The smaller the number, the closer the numbers are together.

s=square root of E(xi^2)/n-x bar^2
**note that everything is under the square root

_____________________________________________________

Ex.1: Find the sample standard deviance and variance for: 3 5 6 7 9

xi xi^2

3 9

5 25

6 36

7 49

9 81

add up all the xi^2 numbers and you get 200

now find the mean by adding 3+5+6+7+9 =30/5 =6

sqaure root of 200/5 - 6^2 = square root of 4 = 2

sample standard deviance=2

variance=4