STAT 35000 Lecture Notes - Lecture 2: Interquartile Range, Standard Deviation, Box Plot
30 Jun 2017
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Discrete random variables: formulae, mean = (cid:894) xi(cid:895)/n, median: if n is odd then median (m) = value of ((n + 1)/2)th item term. If n is even, then there is no single middle value; the median is then usually defined to be the mean of the two middle values: q1 = (d1)th element. Where d1 = n/4: q3 = (d4)th element. Interquartile range (iqr) = q3 q1: standard deviation = variance = 1/(n-1) (xi x)2, five number summary: Consists of: median, minimum, maximum, q1, q3, representing mean and median on skewed data, outliers. All observations outside this range is an outlier: boxplots: Purpose: a simple graphical device to display the overall shape of a distribution, including the outliers. Steps to draw a boxplot: calculate q1, median, q3 and the 1. 5 iqr outlier limits. (cid:1006). Draw a straight line from q1 to either the smallest observation or the q1-1. 5 iqr lower outlier bound, whichever is larger.
