1. 6-8 Measures of Central Tendency and Variation Objective Find measures of central tendency and measures of variation for statistical data. Examine the effects of outliers on statistical data.

2. The symbol commonly used to represent the mean is x, or “x bar.” The symbol for standard deviation is the lowercase Greek letter sigma, σ. Reading Math Small standard deviations indicate data clustered near the mean Large standard deviations indicate data is spread out

3. Finding Standard Deviation

4. Example 1: Finding the Mean and Standard Deviation Find the mean and standard deviation for the data set of the number of people getting on and off a bus for several stops. {6, 8, 7, 5, 9} Step 1 Find the mean. Step 2 Find the difference between the mean and each data value, and square it. Data value (x)68759

5. Example 1: Finding the Mean and Standard Deviation Find the mean and standard deviation for the data set of the number of people getting on and off a bus for several stops. {6, 8, 7, 5, 9} Step 1 Find the mean. Step 2 Find the difference between the mean and each data value, and square it. Data value (x)68759 0 01 1 1 -2 4 2 4

6. Example 1 Continued Step 3 Find the variance. Find the average of the last row of the table Step 4 Find the standard deviation. The standard deviation is the square root of the variance Data value (x)68759 0 01 1 1 -2 4 2 4

7. Example 1 Continued Step 3 Find the variance. Find the average of the last row of the table Step 4 Find the standard deviation. The standard deviation is the square root of the variance Data value (x)68759 0 01 1 1 -2 4 2 4

8. Example 2 Find the mean and standard deviation for the data set of the number of elevator stops for several rides. {0, 4, 2, 1, 6, 5} Step 1 Find the mean. Step 2 Find the difference between the mean and each data value, and square it. Data value (x)042165

9. Example 2 Find the mean and standard deviation for the data set of the number of elevator stops for several rides. {0, 4, 2, 1, 6, 5} Step 1 Find the mean. Step 2 Find the difference between the mean and each data value, and square it. Data value (x)042165 -3 11 1 9 -2 4 2 4 3 9

10. Example 2 Continued Find the average of the last row of the table Step 4 Find the standard deviation. The standard deviation is the square root of the variance Data value (x)042165 -3 11 1 9 -2 4 2 4 3 9 Step 3 Find the variance.

11. Example 2 Continued Find the average of the last row of the table Step 4 Find the standard deviation. The standard deviation is the square root of the variance Data value (x)042165 -3 11 1 9 -2 4 2 4 3 9 Step 3 Find the variance.

12. Classwork/Homework 6-8 Worksheet