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Displaying and Summarizing Quantitative Variable

Displaying and Summarizing Quantitative Variable. Ch. 4. Quantitative Data. A quantitative variable is a measured variable (with units ) that answers questions about the quantity of what is being measured. (e.g. income ($), height (inches), weight (pounds)).

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Displaying and Summarizing Quantitative Variable

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  1. Displaying and Summarizing Quantitative Variable Ch. 4

  2. Quantitative Data • A quantitative variable is a measured variable (with units) that answers questions about the quantity of what is being measured. (e.g. income ($), height (inches), weight (pounds)) • The data are values of a quantitative variable whose units are known Quantitative Data Condition

  3. Barry Bonds’ HRs Who: MLB Seasons from 1986 to 2007 What: Barry Bonds’ HRs (HRs) When: From 1986 to 2007 Where: Cities with MLB teams Why: Mr. Gray likes baseball and needed an example How: Data was gathered from baseball-reference.com

  4. What to look for When you describe a distribution alwaysdescribe the • Shape • Center • Spread

  5. Center“One number to rule them all” • When the distribution is skewed or has outliers, use the median Median -- the middle number when the set is ordered • If there is an even number of data values, the median is the average of the two middle values Has the same units as the data! • When the distribution is unimodal and symmetric, use the mean Mean -- the average of the data set • The “balancing” point of the data Has the same units as the data!

  6. Mean • The (sample) mean is the arithmetic average of the values in a sample

  7. Spread • When the distribution is skewed or has outliers, use the IQR Interquartile Range (IQR) • The difference between quartile 3 and quartile 1 • IQR = Q3 – Q1 Has the same units as the data! • When the distribution is unimodal and symmetric, use the standard deviation Standard Deviation – the square root of the sum of the squared differences from the mean Has the same units as the data!

  8. The Path to Standard Deviation • Deviation from the mean -- the difference of the data value from the mean of the data set • (Sample) Variance -- the sum of the squared deviations from the mean divided by

  9. The Path to Standard Deviation (cont.) • (Sample) Standard Deviation -- the square root of the sample variance

  10. Barry Bonds Summary Statistics • Median: 34 HRs • IQR: 20 HRs • Mean: 34.6 HRs • SD: 14.0 HRs

  11. Three Rules of Data Analysis • Make a picture • Make a picture • Make a picture

  12. Stem and Leaf Diagram • An effective way to display quantitative data when the data set is not too large • Stem – the beginning digit(s) of the data value • Leaf – the final digit(s) of the data value

  13. Histogram • When to use: Number of variables: 1 Data type: quantitative data Purpose: displaying data distribution Include a key

  14. Stem and Leaf Barry Bonds HRs 7|3 represents 73

  15. Stem and Leaf Albert Pujols RBIs 9|9 represents 99

  16. Stem and Leaf 7|3 represents 73

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