ECON 2B03 Lecture Notes - Lecture 5: Frequency Distribution, Kurtosis, Normal Distribution

• School: McMaster University
• Department: Economics
• Course: ECON 2B03
• Professor: Jeff Racine

Document Summary

Equals the difference between the largest and smallest observation in a data set (in r we could use the range() function) Measure difference between 2 values in the ordered array (called fractiles") Interquartile range: difference between 3rd and 1st quartiles (contains middle 50% of data) In r we use the iqr() and quantile() functions. Quantile(x, seq(0,1, by = 0. 25)) ## compute quartiles. A frequency distribution"s degree of distortion from horizontal symmetry. Pearson"s (first) coefficient of skewness is (we want to know is it +/-?) Skewness = (mean mode) / standard deviation. For right-skewed distributions the mean is bigger than the median which is bigger than the mode (for left-skewed just the opposite holds) Kurtosis = n i=1 ( x i x )4. In order to compute certain higher-order moments (e. g. skewness and kurtosis) of a quantitative variable we need to install an optional r package.