1. Notes – Standard Deviation, Variance, and MAD
Algebra 1 Notes
Notes – Standard Deviation, Variance, and MAD

2. Definition of Variance
In a data set, the variance is the mean of the squares of the deviations.
Variance for Population: sigma squared
E represents the sum
x is a single data entry
u is the mean N is the number of data

3. Definition of Standard Deviation
In a data set, the standard deviation is the square root of the variance.
Standard Deviation for Population: sigma
E represents the sum
x is a single data entry
u is the mean N is the number of data

4. Important Note
We have been informed that we will calculate all statistics using the formulas for POPULATION.

5. Example 1: Calculate the variance and standard deviation.
DATA
100 95 80 70 50 30

6. Calculator Directions for Mean, Median, and Standard Deviation
Enter the data
STAT
Edit
Enter numbers into List 1 (L1)
Calculate mean, median, standard deviation
CALC
1-VAR Stats
ENTER
The mean will be displayed as
The standard deviation will be displayed as
You will need to scroll down to get to the median. It will be displayed as Med
The Variance will not be displayed on the screen; it must be calculated by squaring the standard deviation.
The range will not be displayed on the screen; it must be calculated by subtracting: maxX – minX.

7. Example 1: Calculate the variance and standard deviation.
DATA
100
100 – =
(24.375)^2 =
594.14 95
95 – =
375.39 80
4.375
19.141 70
-5.625
31.641 50
-25.63
656.64 30
-45.63
2081.6

8. Definition of Mean Absolute Deviation
In a data set, the mean absolute deviation (MAD) is the mean of the absolute value of the deviations.
MAD for Population
E represents the sum
x is a single data entry
u is the mean.
N is the number of data

9. Example 2: Calculate the mean absolute deviation.
DATA
100 95 80 70 50 30

10. Calculator Directions for Mean Absolute Deviation
Enter the data
STAT
Edit
Enter numbers into List 1 (L1)
Find the mean of the data points,
CALC
1-VAR Stats
ENTER
In List 2 (L2), subtract the mean from each data point in L1 and then take the absolute value of the answer.
Use the arrow keys to move cursor so that L2 is highlighted
2nd Zero ENTER 2nd 1 minus VARS 5 2 ) ENTER
Find the mean of the values in L2
1-VAR Stats 2nd 2

11. Example 2: Calculate the mean absolute deviation.
DATA
100
100 – =
24.375 95
95 – =
19.375 80
4.375 70
-5.625
5.625 50
-25.63
25.63 30
-45.63
45.63