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

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

3. Unit 1.3 – Descriptive Statistics Describing Data – SOCS Shape – See the next slide Outliers – Identify the outliers Center – Mean and Median Spread – Standard Deviation 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9

4. 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 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9

5. Unit 1.3 – Descriptive Statistics More on Symmetry… Examples of perfect symmetry:Fairly Symmetric:Not very symmetric: 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9

6. Unit 1.3 – Descriptive Statistics Describing Data – SOCS Shape – This distribution would be fairly symmetric but the outlier is skewing it right. Outliers – 104.4 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 9.577 and the range is 36. 70.277.474.790.9104.4 81.985.586.4 75.6 74.768.494.584.681.9

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

8. Unit 1.3 – Descriptive Statistics Time Plots with Trends

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

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

11. 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 40-442 45-496 50-5413 55-5912 60-647 65-693 ClassFrequencyRelative Frequency 40-442 45-496 50-5413 55-5912 60-647 65-693 2 / 43 = 4.651%

12. 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. 40-4424.651% 45-49613.953% 50-541330.233% 55-591227.907$ 60-64716.279% 65-6936.977% ClassFreq.Rel. Freq.Cumulative Frequency 40-4424.651% 45-49613.953% 50-541330.233% 55-591227.907$ 60-64716.279% 65-6936.977% 40

13. 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 40-4424.651%2 45-49613.953%8 50-541330.233%21 55-591227.907$33 60-64716.279%40 65-6936.977%43 ClassFreq.Rel. Freq.Cumulative Frequency Relative Cumulative Frequency 40-4424.651%2 45-49613.953%8 50-541330.233%21 55-591227.907$33 60-64716.279%40 65-6936.977%43 40 / 43 = 93.023%

14. Unit 1.3 – Descriptive Statistics Complete Frequency Table ClassFreq.Rel. Freq.Cumulative Frequency Relative Cumulative Frequency 40-4424.651%2 45-49613.953%818.605% 50-541330.233%2148.837% 55-591227.907$3376.744% 60-64716.279%4093.023% 65-6936.977%43100%

15. Unit 1.3 – Descriptive Statistics Complete Frequency Table to O-give ClassFreq.Rel. Freq.Cumulative Frequency Relative Cumulative Frequency 40-4424.651%2 45-49613.953%818.605% 50-541330.233%2148.837% 55-591227.907$3376.744% 60-64716.279%4093.023% 65-6936.977%43100%

16. Unit 1.3 – Descriptive Statistics Complete Frequency Table to O-give ClassFreq.Rel. Freq.Cumulative Frequency Relative Cumulative Frequency 40-4424.651%2 45-49613.953%818.605% 50-541330.233%2148.837% 55-591227.907$3376.744% 60-64716.279%4093.023% 65-6936.977%43100%

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

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

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

20. 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?