1. Measures of Variation pages 123-129

2. Route A Route B Which route is better? In this example both routes have a mean of 31. We need another method for analyzing statistics. 15 26 30 39 45 29 30 31 32 33

3. Range is the highest data value minus the lowest data value. R = (highest value - lowest value) We need methods for calculating variability and consistency! Range is a good method for calculating how spread out a single set of data is.

4. x We will calculate the variance and standard deviation of Route A 15 26 30 39 45

5. x Variance and Standard Deviation for Route B. 29 30 31 32 33

6. s = Sample Standard Deviation Population Standard Deviation = Variance is simply the value obtained immediately before finding the square root.

7. Variance is the average of the squares of the distance each value is from the mean. Standard deviation is the square root of the variance, it is a measure of how spread out your data are. More uses on next slide...

8. · To determine the spread of the data. ·To determine the consistency of a variable. ·To determine the number of data values that fall within a specified interval in a distribution (Chebyshev’s Theorem). ·Used in inferential statistics.

9. Additional worked examples

10. Population set of data!!!

11. Sample set of data!!!