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Numerical Measures

Numerical Measures. Central Tendency, Variation, Relative Standing, Skewness , Box Plots. Parameter vs. Statistic. Parameter: numerical value that describes the population Statistic: numerical value that describes the sample. I. Measures of Central Tendency. Mean. Example.

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Numerical Measures

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  1. Numerical Measures Central Tendency, Variation, Relative Standing, Skewness, Box Plots

  2. Parameter vs. Statistic • Parameter: numerical value that describes the population • Statistic: numerical value that describes the sample PLBautista

  3. I. Measures of Central Tendency • Mean PLBautista

  4. Example • The following data shows the number of hours of watching television in a week for a sample of 5 observations: • What is the sample mean? 3 5 7 7 13 PLBautista

  5. I. Measures of Central Tendency • Median • Value “in the middle” of the data set (IMPORTANT: The data must be in increasing order) • For data with even no. of observations: average of the two middle values • More useful for data with extreme values PLBautista

  6. I. Measures of Central Tendency • Mode • Most frequently occurring value • More useful for qualitative data PLBautista

  7. Example • Compute the mean and median for the following data sets: • 96 97 100 100 101 101 105 • 75 77 90 100 108 117 133 PLBautista

  8. II. Measures of Variation/Spread • Range • Variance PLBautista

  9. II. Measures of Variation/Spread • Standard Deviation PLBautista

  10. Coefficient of Variation • Useful for comparing the spread between data sets with different units PLBautista

  11. Exercise For the following data set, compute • Mean • Median • Mode • Range • Variance • Standard deviation • Coefficient of Variation 53 55 57 53 69 70 57 59 52 53 PLBautista

  12. III. Measures of Relative Standing IMPORTANT: For the following, data has to be arranged in increasing order! • Percentiles • The position of the ith percentile is given by • If not an integer, round up! • If is an integer, is the average of the and observation PLBautista

  13. III. Measures of Relative Standing • Deciles • The position of the ithdecileis given by • Quartiles • The position of the ithquartile is given by PLBautista

  14. IV. Measure of Skewness • Skewness is the measure of the distribution of values in the data set PLBautista

  15. http://www.southalabama.edu/coe/bset/johnson/lectures/lec15_files/image014.jpghttp://www.southalabama.edu/coe/bset/johnson/lectures/lec15_files/image014.jpg PLBautista

  16. V. Other Forms of Data Description • Box Plots • Useful for comparing multiple data sets PLBautista

  17. Five-Number Summary • Smallest Value • Q1 • Q2 • Q3 • Largest Value PLBautista

  18. V. Other Forms of Data Description • Stem-and-Leaf Display PLBautista

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