1. Standard Deviation and Z score
Algebra I

2. Standard Deviation
Definition – When looking at a set of data, the distance away from the mean. The center is considered the most ‘typical’. How far from ‘typical’ is the data?

3. Standard Deviation
Some data is more dispersed than others. They have the same mean, but the data is spread out more (or less) than the mean.

4. Greek Symbols
σ – “sigma” symbol for standard deviation. µ - “mu” symbol for mean also sometimes written as x. σ²- “sigma squared” symbol for variance.

5. Standard Deviation Finding standard deviation in the calculator. STAT
EDIT enter data
CALC
1-VarStats
ENTER standard deviation is shown as σx
mean is shown as x

6. Example
Find the standard deviation, mean and variance of the following set of data.
σ =
µ =
σ²=

7. Example
Find the standard deviation, mean and variance of the following set of data.
σ = 5.83
µ = 89.25
σ²= 33.99

8. Another example
Find the standard deviation, mean and variance for the following set of data:

9. Another example
Find the standard deviation, mean and variance for the following set of data:
σ = 16.94
µ = 65
σ²=

10. Z score
Definition – How many standard deviations above or below the mean. This is given to you on your formula sheet.
x – the value in the data set
µ - mean
σ – standard deviation

11. Z score
Finding z score.
Find the mean and standard deviation in the calculator.
The circled number is the value in the data set to use.
Just plug in the numbers and solve.

12. Z score
Finding z score.
First, find the mean and standard deviation
z = x - µ σ

13. Z score
Finding z score.
X = 65 (the element given)
µ = 69.29
σ = 3.92
Now substitute these values into the formula.
z = x - µ σ

14. Z score Finding z score. 72 63 70 68 65 72 75 x = 65 µ = 69.29
x = 65
µ = 69.29
σ = 3.92
z = x - µ z = 65 – = -1.09 σ