Variability!

Hope you all had a fantastic weekend!

Well, this week in class we learned about Variability.

The variance, denoted 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
this E looking thing=sum
xi=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

Example 1:
Compute the mean, variance, and standard deviation.
The number of grammatical errors on five daily French quizzes:
10, 8, 7, 5, 5
xi xi^2
10 100
8 64
7 49
5 25
5 25
total=263
n=5
x bar=7
xi^2=263
s=square root of 263/5-7^2
=square root of 263/5-49
=square root of 3.6
=1.90
variance=3.6
standard deviation=1.91
mean=7