2. 3.2 Measures of Variability Objectives: By the end of this section, I will be able to… 1) Understand and calculate the range of a data set. 2) Explain in my own words what a deviation is. 3) Calculate the variance and the standard deviation for a population or a sample.

3. What is variation? It is the spread of the numbers around the mean.

4. Measures of Variation 1. Variance 2. Standard Deviation 3. Range Highest – Lowest

5. Why is VARIATION important? Because less variation means smaller spread in the data, which means 1. More precise estimates 2. Higher confidence in our conclusions about the data

6. Wall Street Journal competition Stocks were chosen by Stocks were chosen by 1. Journal staff randomly throwing darts at a list of the stocks 2. A team of four financial experts 3. The DJIA (Dow Jones Industrial Average)

7. THE RESULTS ARE…

8. Variations and Graphs

9. Measuring V-Span 1. Make a V between your index finger and your middle finger when you spread them as far as possible. 2. Measure to the nearest tenth of a centimeter. Your V-Span = Your V-Span = 3. Compute the group’s mean V-Span. Mean V-Span = Mean V-Span = 4. Now fill out the following chart with your data and find the three values of variation

10. xx-mean (x-mean) 2 Variance = Sum/(n – 1) Put in all of your V-spans as x values. Add rows as necessary. Then use the mean (average V-span) and find the difference between each x value and the mean Square the number you just found… Standard deviation = Square ROOT of the variance

11. Calculator Time Find the variance and standard deviation on your calculator. Find the variance and standard deviation on your calculator.

12. NASCAR TIME NASCAR TIME - link NASCAR TIME On a separate sheet of paper, and one per person – NEATLY complete the following. On a separate sheet of paper, and one per person – NEATLY complete the following. Find the mean, median, mode, range, variance, and standard deviation of NASCAR points of the top 10 drivers for 2010. Find the mean, median, mode, range, variance, and standard deviation of NASCAR points of the top 10 drivers for 2010.