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Describing Distributions SHAPES Unimodal Multimodal Bimodal Uniform SHAPES (cont’d) GENERAL SHAPES of DATA Unimodal • test scores Multimodal • favorite numbers Bimodal • height (M & F) Uniform • # pencils manufactured each day at factory MEASURES OF CENTER MEDIAN • middle number of all data values when ordered ascending or descending • NOT affected by value of data • Divides histogram into equal areas MEAN • arithmetic average • IS affected by value of data • the “balancing point” of the histogram MODE • data value repeated most • seen as humps in a histogram CALCULATING THE MEAN Pronounced “y-bar” 𝑡𝑜𝑡𝑎𝑙 𝑦 𝑦= = 𝑛 𝑛 WHICH CENTER WHERE? Nominal – categorical data with no rank (i.e. sex, race, hair color) Ordinal – categorical data with ranking (i.e. level of education, economic status) Interval – quantitative data MEASURES OF SPREAD RANGE • = max – min • good to mention for many distributions IQR • = Q3 – Q1 • use with skewed distribution • sometimes good to mention with symmetric distribution STANDARD DEVIATION • use with symmetric distribution CALCULATING STANDARD DEVIATION Variance: 2 𝑦) (𝑦 − 2 𝑠 = 𝑛−1 Standard Deviation: 𝑠= 2 𝑦) (𝑦 − 𝑛−1 Pg. 84 - Summary