ECON1203 Lecture Notes - Lecture 2: Standard Deviation, Square Root, Unimodality
Week 2 – Numerical Summaries
Key features of a single variable
• Location, spread, relative location, skewness
Key features of two variables
• Measures of (linear) association
Measures of location
• Parameter: describes a key feature of a population
• Statistic: describes a key feature of a sample
• A atural easure of loatio or etral tede is the aritheti ea
• Median: middle value of ordered observations
Depends on ranks of observations, not absolute values
• Mode: most frequently occurring value(s)
Modal lass – previously defined in the context of unimodal histograms
Measures of variability
• Range = maximum – minimum
Simple, but potentially misleading
• Variance: most common measure of variability
Measures average squared distance from the mean
Square root variance to get standard deviation (answer format)
Coefficient of variation, cv = s / (x bar)
• Where s = standard deviation
• Measure of relative variability
Standardising data
• Create a trasfored ariale ith zero ea ad uit i.e. 1 ariae fro a
original quantitative variable
• Transformed variable is free of units
• Called calculating Z-scores (one Z-score per observation)
Calculate (Observation – Mean) / Standard deviation
Implies that: x% is y standard deviations above the mean return
Measure of relative location
• Median relies on a ranking of observations to measure location
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