Unit 1.3 – Descriptive Statistics Describing DataSOCSSkewSymmetric Time PlotsSeasonalTrendsBox and Whisker Variation 5-Number Summary O-givesRelative FrequencyCumulativeRelative CumulativeFrequency Density CurvesNormal DistributionPercentilesZ-scores

Unit 1.3 – Descriptive Statistics Part 1 Describing Data SOCS Skew Symmetric

Unit 1.3 – Descriptive Statistics Describing Data – SOCS Shape – See the next slide Outliers – Identify the outliers Center – Mean and Median Spread – Standard Deviation

Unit 1.3 – Descriptive Statistics Shape Skew LeftSkew RightSymmetric Typically due to an outlier Typically due to an outlierCan be folded at the median on the left. Tail is on the left.on the right. Tail is on the right.to produce side to side symmetry

Unit 1.3 – Descriptive Statistics More on Symmetry… Examples of perfect symmetry:Fairly Symmetric:Not very symmetric:

Unit 1.3 – Descriptive Statistics Describing Data – SOCS Shape – This distribution would be fairly symmetric but the outlier is skewing it right. Outliers – is an outlier to the right. Center – Mean and Median The mean (82.5) is higher than the median (81.9). Spread – Standard Deviation The standard dev is and the range is

Unit 1.3 – Descriptive Statistics Part 1 continued… Time Plots Trends Seasonal Variation

Unit 1.3 – Descriptive Statistics Time Plots with Trends

Unit 1.3 – Descriptive Statistics Time Plots with Seasonal Variation Note that some also have trend

Unit 1.3 – Descriptive Statistics Part 2 Relative Frequency Cumulative Frequency Relative Cumulative Frequency Ogives Percentiles

Unit 1.3 – Descriptive Statistics Ages of US Presidents Frequency Relative Frequency To calculate Relative Frequency, simply divide each Frequency value by the number of individuals (43). ClassFrequency ClassFrequencyRelative Frequency / 43 = 4.651%

Unit 1.3 – Descriptive Statistics Cumulative Frequency To calculate Cumulative Frequency for any particular row, sum the Frequency cells for that row and all previous rows. ClassFreq.Rel. Freq % % % $ % % ClassFreq.Rel. Freq.Cumulative Frequency % % % $ % % 40

Unit 1.3 – Descriptive Statistics Relative Cumulative Frequency To calculate the Relative Cumulative Frequency, simply divide the corresponding Cumulative Frequency by the number of individuals. ClassFreq.Rel. Freq.Cumulative Frequency % % % $ % %43 ClassFreq.Rel. Freq.Cumulative Frequency Relative Cumulative Frequency % % % $ % %43 40 / 43 = %

Unit 1.3 – Descriptive Statistics Complete Frequency Table ClassFreq.Rel. Freq.Cumulative Frequency Relative Cumulative Frequency % % % % % $ % % % %43100%

Unit 1.3 – Descriptive Statistics Complete Frequency Table to O-give ClassFreq.Rel. Freq.Cumulative Frequency Relative Cumulative Frequency % % % % % $ % % % %43100%

Unit 1.3 – Descriptive Statistics Complete Frequency Table to O-give ClassFreq.Rel. Freq.Cumulative Frequency Relative Cumulative Frequency % % % % % $ % % % %43100%

Unit 1.3 – Descriptive Statistics Interpreting an O-give What percentile was Bill Clinton in for age of Presidents at inauguration?

Unit 1.3 – Descriptive Statistics Interpreting an O-give What percentile was Bill Clinton in for age of Presidents at inauguration?

Unit 1.3 – Descriptive Statistics Interpreting an O-give Which percent of presidents were younger than 58 years old at inauguration?

Unit 1.3 – Descriptive Statistics Interpreting an O-give If a presidential candidate is said to be in the 80 th percentile for Age for all former presidents, how old are they?