1. Review: Measures of Dispersion Objectives: Calculate and use measures of dispersion, such as range, mean deviation, variance, and standard deviation.

2. Measures of Dispersion Measures of dispersion shows how spread out the data is. Range and Interquartile Range –Not very reliable (only depends on two variables) Mean Deviation –The average amount that the values in a data set differ from the mean Variance –The deviation of all values from the mean Standard Deviation –The square root of the variance

3. Variance Lower case sigma Each data value Mean n Number of terms in the data set A smaller variance means the data is close to the mean. The data values are a good representation and are reliable.

4. Standard Deviation The standard deviation is the square root of the variance. A smaller standard deviation also represents more reliable data.

5. Example 1 The following are a sample of a student’s test scores in math and history: Math: 85, 91, 96, 85, 93 History: 82, 92, 100, 77, 84 Find the mean, range, variance and standard deviation for each class.

6. Example 1 Math Scores: 85, 91, 96, 85, 93 XiXi X i - X(X i – X) 2 Total 96 – 85 = 11 Range: Variance: Mean: 90 85 91 96 85 93 85-90 -525 91-90 96-90 85-90 93-90 1 6 -5 3 1 36 25 9 96

7. Example 1 XiXi X i - X(X i – X) 2 Total Variance: 85 91 96 85 93 -5 25 1 6 5 3 1 36 25 9 96 = 19.2

8. Example 1 Math Scores: 85, 91, 96, 85, 93 Mean: 90 Range: 11 Variance: 19.2 Standard Deviation

9. Example 1 Now, you do the History Scores: XiXi X i - X(X i – X) 2 Total Range: Variance: Mean: Standard Deviation: 87 23 8.1 65.6

10. What do these values mean? Compare the Variance and Standard Deviation for the Math and History Scores: Math 19.2 4.4 History 65.6 8.1 The values for the math scores are smaller, which means they are more and reliableconsistent.