Class 03 - 2016-09-26 - Descriptive Stats

Notes on Slides

• Best Practices to describing data: Report at least one measure of:

LOCATION

• The center of the data

1. mean: The average. Outliers heavily influence this stat
   • x-bar for sample
   • mu for population
2. median: The middle of the dataset. When typical representative data is desired.
3. mode: Most frequent measurement

DISPERSION

• Relative to what? the center? Comparison with a past time period?

1. Range: Delta, max-min
2. Variance: Measured in square units
3. Standard deviation: sqrt of the variance
   • s for sample
   • sigma for population

Relative Measures of Location

• using x-bar and s
• Chebyshev Rule: 75% of data falls within 2 stdevs
• Empirical Rule: If Normal distribution (bell shaped) 95% of data within 2 stdevs
  • 1-sigma = 68% of all data points
  • 2-sigma = 95% of all data points
  • 3-sigma = 99% of all data points
• To visualize use Histogram, dotscale, or box plot

Skewness

• Symmetrical, positive or negative

Making Comparisons

• Descriptive Statistics:
  • Mean, median, mode, min, max, range, stdev, coef. of variation, count
• Five number summaries / boxplot
  • Tell you the skewness
  • Min, 1st quartile, MEDIAN (not mean), 3rd quartile, maximum
• Coeff. of variation
  • measuring relative variability between datasets
  • STDEV * 100 = what percent of the sample mean
• Bollinger band - +/- 2 stdev