1. Statistics Standard: S-ID
Objectives: Find the measures of variation

2. Key terms 1. Range 2. Variance 3. Standard deviation
4. Inter quartile range
5. Coefficient of variation
6. Outliers
7. Symmetric data Skewed data

3. Descriptive statistics
Describing data with numbers: measures of variation

4. What to describe? What is the “location” or “center” of the data?
How do the data vary from its center?

5. Measures of Variability
Range
Variance and standard deviation
Coefficient of variation
Inter quartile range
All of these measures are appropriate for measurement data only.

6. Range The difference between largest and smallest data point.
Highly affected by outliers.
Best for symmetric data with no outliers.

7. The Importance of Measuring Variability
Central tendency - Numbers that describe what is typical or average (central) in a distribution
Measures of Variability - Numbers that describe diversity or variability in the distribution.

8. The Range Range = highest score - lowest score
Range – A measure of variation in interval-ratio variables. It is the difference between the highest (maximum) and the lowest (minimum) scores in the distribution.
Range is a good thing to look at to make sure your data are as you expect them to be.

9. Measures of Variation Standard Deviation of a Population
We will label the population variance to be σ2
And define σ2 = Σi(xi – μ)2/N
Where
μ is the population mean
N is the size of the population
Σi(xi – μ)2 is the sum of the squares of the difference between each item in the population and the mean.

10. Measures of Variation
Suppose a student receives the following quiz grades:
{82, 68, 74, 86, 90, 88, 62, 75, 80, 55}. Find the population variance and standard deviation.

11. Measures of Variation
If we display the data on a dot plot, we can visualize the use of the standard deviation as a measure of variation in the data
{82, 68, 74, 86, 90, 88, 62, 75, 80, 55}
μ = 76 σ σ x x x x x x x x x x
Mean = 76

12. Choosing Appropriate Measure of Variability
If data are symmetric, with no serious outliers, use range or standard deviation.
If data are skewed, and/or have serious outliers, use IQR.
If comparing variation across two data sets, use coefficient of variation.