*Standard Deviation

*Measures of Variation

*Measures of variation describe how data in a data set is spread out.

*Common measures include range and interquartile range.

*Variance and standard deviation are measures showing how much data varies from the mean.

*the Greek letter “Sigma” represents standard deviation.

* (sigma squared) represents variance

*Finding Variance and Standard Deviation

1. Find the mean, of the n values in a data set.

2. Find the difference, , between each value x and the mean.

3. Square each difference

4. Find the average (mean) of these squares. This is the variance.

5. Take the square root of the variance to find the standard deviation.

*Example

Find the mean, variance, and standard deviation of these values: 6.9, 8.7, 7.6, 4.8, 9.0

Sum=

*Another Example

Find the mean, variance, and standard deviation of : 52, 63, 65, 77, 80, 82

Sum=

*Using a Calculator

Decade

1 2 3 4 5 6 7 8 9 10

11

12

13

14 15

Strikes 19 15 20 22 21 18 21

13

19

24

17

14

12 15 14

The table displays the number of U.S. hurricane strikes by decade from the years 1851 to 2000. What are the mean and standard deviation for thisdata set?

*Another Calculator

Year

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

# 4 4 3 11 10 3 10 8 8 9 4 7 9 14 5

The table displays the number of hurricanes in the Atlantic Ocean from 1992 to 2006. What are the mean and standard deviation?

*Describing Data

Using the previous information, within how many standard deviations from the mean do all of the values fall?

Decade

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Strikes 19

15

20

22

21

18

21

13

19 24 17 14 12 15 14