Unit 1.2 – Descriptive Statistics Standard DeviationDegrees of FreedomVariance Rule Data TypesIndividualsCategoricalQuantitative Graphing Categorical VariablesBar GraphsPie Charts Graphing Quantitative VariablesDot PlotsStem PlotsHistograms

Unit 1.2 – Descriptive Statistics Part 1 Standard Deviation Degrees of Freedom Variance Rule

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

Unit 1 – Descriptive Statistics Understanding the Rule 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

Unit 1 – Descriptive Statistics Ex 1. Mean = 82.5 Standard Deviation = There is a major assumption being made when using the 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)

Unit 1 – Descriptive Statistics Ex 1. Mean = 82.5 Standard Deviation = Checking for Understanding… What percent of days can we expect to have a temperature lower than ˚ F? 2.What percent of days can we expect to have a temperature lower than ˚ 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 ˚ F?

Unit 1 – Descriptive Statistics Ex 1. Mean = 82.5 Standard Deviation = Checking for Understanding… continued… What percent of days can we expect to have a temperature higher than ˚ F? 2.What percent of days can we expect to have a temperature higher than ˚ 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 ˚ F?

Unit 1 – Descriptive Statistics Ex 1. Mean = 82.5 Standard Deviation = Checking for Understanding… continued… What percent of days can we expect to have a temperature between ˚ F and ˚ F ? 2.What percent of days can we expect to have a temperature between ˚ F and ˚ F ? 3.What percent of days can we expect to have a temperature between ˚ F and ˚ F ? 4.What percent of days can we expect to have a temperature between ˚ F and ˚ F ?

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

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

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

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

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

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

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

Unit 1.2 – Descriptive Statistics Categorical Data - Bar Graph

Unit 1.2 – Descriptive Statistics Categorical Data – Pie Chart

Unit 1.2 – Descriptive Statistics Quantitative Data – Dot Plot

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

Unit 1.2 – Descriptive Statistics Quantitative Data – Histogram

Unit 1.2 – Descriptive Statistics Quantitative Data – Histogram