1. Standard Deviation

2. The Standard Deviation measures how much variation there is from the mean (average). A low standard deviation indicates that the data points tend to be very close to the mean. A high standard deviation indicates that the data is spread out over a large range of values.
Formula:

3. Empirical Rule

4. How to calculate Standard Deviation (using calculator)
Find standard deviation of the following set of numbers: 5, 3, 1, 8, 2
Press MODE and select 2 for statistics mode, then select 1 for (1 – var)
Input numbers and press = after each input e.g. 5 =, 3 =, etc…
Press AC to clear and then SHIFT and 1 to go to menu
Select 4 to get statistics on variables, then select 2 and =, this is your answer for the mean.
Press AC to clear and then SHIFT and 1 to go to menu.
Select 5 to get statistics on variables then 3 and =, this is the Standard Deviation (σ)

5. Example 1
Calculate the mean and standard deviation of the following numbers: , 9, 10, 12, Mode, 2, 1, input numbers (=)
Calculate the mean: AC, SHIFT, 1, 4, 2, =
Calculate the standard deviation AC, SHIFT, 1, 4, 3, =

6. How to calculate Standard Deviation of frequency distribution
The following frequency distribution table shows the number of birdies scored per round of golf.
Find the mean and standard deviation, correct to one decimal place.
Press MODE and select 2 for statistics mode, then select 1 for (1 – var)
Input numbers and frequencies and press = after each input
No. of Birdies 1 2 3 4 5 6
Frequency

7. Continued. . . Press AC to clear and then SHIFT and 1 to go to menu
Select 4 to get statistics on variables, then select 2 and =, this is your answer for the mean. (AC, SHIFT, 1, 4, 2, =)
Press AC to clear and then SHIFT and 1 to go to menu.
Select 5 to get statistics on variables then 3 and =, this is the Standard Deviation (σ) (AC, SHIFT, 1, 4, 3, =)

8. Example 2
Calculate the mean and standard deviation of the following, give answer correct to 1 decimal place: Mode, 2, 1, input numbers (=)
Calculate the mean: AC, SHIFT, 1, 4, 2, =
Calculate the standard deviation AC, SHIFT, 1, 4, 3, =
Time
12-14
15-17
18-20
21-23
Frequency 3 5 8 4