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Professor FriedmanLecture Notes: Descriptive StatisticsPage 1 TOPIC: Descriptive Statistics Single Variable I. Numerical data – summary measurements A. Measures of Location 1. Measures of central tendency Mean; Median; Mode 2. Quantiles - measures of noncentral tendency Quartiles; Percentiles B. Measures of Dispersion Range; Interquartile range; Variance; Standard Deviation; Coefficient of Variation C. Measures of Shape Skewness 5-number summary Box-and-whisker Stem-and-leaf D. Standardizing Data II. Categorical data A. Frequencies (also useful for grouped numerical data) Frequency Distribution Percentage Distribution Cumulative Distribution Histogram Polygon Ogive B. Charts Bar chart Pie chart Pareto diagram
Professor FriedmanLecture Notes: Descriptive StatisticsPage 2 Summary Measures Measures of Location Measures of Central Tendency Mean Median Mode The sample mean is the sum of all the observations divided by the number of observations: X= nXXXXn321+…+++or X= nXnii∑=1where ∑Xiis the same as X1+ X2+ X3+ … + Xn Example: 1 2 2 4 5 10 X= 24 / 6 = 4.0
Lecture Notes: Descriptive StatisticsPage 3
Professor FriedmanLecture Notes: Descriptive StatisticsPage 4 EXAMPLE: 0 2 3 5 ←20 99 100 Median = 5 n=7 Since n is odd, the median is the (n+1)/2 ordered observation, or the 4thobservation. EXAMPLE n = 6 10 20 30 40 50 60 Median = 35
Professor FriedmanLecture Notes: Descriptive StatisticsPage 5 EXAMPLE: Exam scores 0 0 0 ←0 100 What is the mean? Suppose the prof lets students know the following grading policy: Anyone who got the mean or better gets an A for the course; anyone who got below the mean fails. Are we happy or unhappy? Note that the mean and median are UNIQUE for a given set of data.