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Review Notes highlighted - STAT 2120 Notes on Topic 1...

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STAT 2120, Notes on Topic 1, Spring 2010 Introduction to Examining Distributions: A variable records characteristics of individuals ( i.e. , objects of interest) in its values. Classify a variable by its possible values: o Categorical: records group labels; numeric labels mean nothing, except possible order. o Quantitative: records meaningful numbers; may be discrete or continuous A time series is a record of values across time. A variable’s distribution describes the counts or relative proportions of its values. Exploratory data analysis seeks to describe distributions and relationships in data. Displaying a distribution with graphs: Bar graphs and pie charts describe the distribution of a categorical variable. o Bar graphs emphasize counts; pie charts, proportions. o A Pareto chart is a bar graph with categories ordered by decreasing frequency. Histograms are essentially bar graphs of a quantitative variable. o Bar-widths are not absolute; use equal bar- widths and “eyeball” for best picture. o Look for overall pattern, shape center, spread, deviations in shape, and “outlier” deviations. o A symmetric distribution is such that its histogram mirrors itself about its center. o A right- or left-skewed distribution shows a long tail to the right or left in its histogram. Stemplots are back-of-the-envelope histograms drawn with the digits of quantitative values o “Stem” digits define bars; “leaf” digits display counts and sub-counts. o Customize by rounding digits and splitting stems. Time plots graph time series values by time. o Emphasize patterns of change over time, such as trends and seasonal variations. o Some time plots are seasonally adjusted. Describing distributions with numbers: Denote by     the values of observations. th percentile is a number such that percent of values fall on or below. Describe a distribution with numerical summaries of shape, center, and spread. A summary is resistant if it is insensitive to changes in skewness or extreme values. Measure of center: mean, o     , the arithmetic average. o is not resistant. Measure of center: median, o is the 50 th percentile. o Calculate as the middle value or average of two middle values. o is resistant. Measure of spread: extreme values o Smallest and largest values o Extreme values are not resistant. Measure of spread: quartiles, and o is the 25 th percentile; is the 75 th percentile o Calculate and as medians of values falling to the left or right of (but not on) . o and are resistant. Measure of spread: standard deviation, o    , where      , a rescaled average of squared-deviations from .
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