1. Unit 1.2 – Descriptive Statistics Standard DeviationDegrees of FreedomVariance68-95-99.7 Rule Data TypesIndividualsCategoricalQuantitative Graphing Categorical VariablesBar GraphsPie Charts Graphing Quantitative VariablesDot PlotsStem PlotsHistograms

2. Unit 1.2 – Descriptive Statistics Part 1 Standard Deviation Degrees of Freedom Variance 68-95-99.7 Rule

3. Unit 1 – Descriptive Statistics Our data set on temperature readings has been modified using a transformation and is shown below: The most commonly used measure of spread in AP Statistics is standard deviation. Find both the variance and standard deviation for the data set above. Make sure you understand the relationship between variance and standard deviation. The degrees of freedom is simply n – 1 where n is the sample size. We will use n and n – 1 very often throughout the year. 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9

4. Unit 1 – Descriptive Statistics Understanding the 68-95-99.7 Rule 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9 Often times we will talk about a data point or observation with respect to the mean and standard deviation. Ex 1. Mean = 82.5 Standard Deviation = 9.577

5. Unit 1 – Descriptive Statistics 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9 Ex 1. Mean = 82.5 Standard Deviation = 9.577 There is a major assumption being made when using the 68-95 Rule and that is that the data is normally distributed. We will talk more about this idea in Unit 1.3 but for now, know that this means the distribution is spread about the mean proportionally to it’s standard deviation. In otherwords N(x,s) 82.563.346101.654 111.231 72.923 92.077 53.769

6. Unit 1 – Descriptive Statistics 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9 Ex 1. Mean = 82.5 Standard Deviation = 9.577 Checking for Understanding… 82.563.346101.654 111.231 72.923 92.077 53.769 1.What percent of days can we expect to have a temperature lower than 53.769˚ F? 2.What percent of days can we expect to have a temperature lower than 72.923˚ F? 3.What percent of days can we expect to have a temperature lower than 82.5˚ F? 4.What percent of days can we expect to have a temperature lower than 101.654˚ F?

7. Unit 1 – Descriptive Statistics 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9 Ex 1. Mean = 82.5 Standard Deviation = 9.577 Checking for Understanding… continued… 82.563.346101.654 111.231 72.923 92.077 53.769 1.What percent of days can we expect to have a temperature higher than 63.346˚ F? 2.What percent of days can we expect to have a temperature higher than 72.923˚ F? 3.What percent of days can we expect to have a temperature higher than 82.5˚ F? 4.What percent of days can we expect to have a temperature higher than 92.077˚ F?

8. Unit 1 – Descriptive Statistics 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9 Ex 1. Mean = 82.5 Standard Deviation = 9.577 Checking for Understanding… continued… 82.563.346101.654 111.231 72.923 92.077 53.769 1.What percent of days can we expect to have a temperature between 72.923˚ F and 92.077˚ F ? 2.What percent of days can we expect to have a temperature between 53.769˚ F and 111.231˚ F ? 3.What percent of days can we expect to have a temperature between 63.346˚ F and 92.077˚ F ? 4.What percent of days can we expect to have a temperature between 92.077˚ F and 111.231˚ F ?

9. Unit 1.2 – Descriptive Statistics Part 2 Data Types Individuals Categorical Quantitative

10. Unit 1.2 – Descriptive Statistics Our next task was to gather more detailed data over a one week period. Our data is shown below: DayLowHighHumidityPrecipitationAir Quality Monday637845%LightGood Tuesday668813%NoFair Wednesday589010%NoPoor Thursday59928%NoPoor Friday609718%NoFair Saturday639615%NoFair Sunday64988%NoPoor

11. Unit 1.2 – Descriptive Statistics 1. Identify the individuals and categories DayLowHighHumidityPrecipitationAir Quality Monday637845%LightGood Tuesday668813%NoFair Wednesday589010%NoPoor Thursday59928%NoPoor Friday609718%NoFair Saturday639615%NoFair Sunday64988%NoPoor

12. Unit 1.2 – Descriptive Statistics 2. Classify each category as categorical or quantitative DayLowHighHumidityPrecipitationAir Quality Monday637845%LightGood Tuesday668813%NoFair Wednesday589010%NoPoor Thursday59928%NoPoor Friday609718%NoFair Saturday639615%NoFair Sunday64988%NoPoor

13. Unit 1.2 – Descriptive Statistics 4. For each column, identify the most appropriate graphing type DayLowHighHumidityPrecipitationAir Quality Monday637845%LightGood Tuesday668813%NoFair Wednesday589010%NoPoor Thursday59928%NoPoor Friday609718%NoFair Saturday639615%NoFair Sunday64988%NoPoor

14. Unit 1.2 – Descriptive Statistics Ticket out the Door 5. Come up with your own example of a data set that includes all 4 vocab words and check with Mr. Newton DayLowHighHumidityPrecipitationAir Quality Monday637845%LightGood Tuesday668813%NoFair Wednesday589010%NoPoor Thursday59928%NoPoor Friday609718%NoFair Saturday639615%NoFair Sunday64988%NoPoor

15. Unit 1.2 – Descriptive Statistics Part 3 Graphing Categorical Variables Bar GraphsPie Charts Graphing Quantitative Variables Dot PlotsStem PlotsHistograms

16. Unit 1.2 – Descriptive Statistics Categorical Data - Bar Graph

17. Unit 1.2 – Descriptive Statistics Categorical Data – Pie Chart

18. Unit 1.2 – Descriptive Statistics Quantitative Data – Dot Plot

19. Unit 1.2 – Descriptive Statistics Quantitative Data – Stem and Leaf Plot

20. Unit 1.2 – Descriptive Statistics Quantitative Data – Histogram

21. Unit 1.2 – Descriptive Statistics Quantitative Data – Histogram