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Describing Distributions. SHAPES. Bimodal. Unimodal. Multimodal. Uniform. GENERAL SHAPES of DATA. Bimodal height (M & F). Unimodal t est scores. Multimodal f avorite numbers. Uniform # pencils manufactured each day at factory. MEASURES OF CENTER. MODE data value repeated most
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SHAPES Bimodal Unimodal Multimodal Uniform
GENERAL SHAPES of DATA Bimodal • height(M & F) Unimodal • test scores Multimodal • favorite numbers Uniform • # pencils manufactured each day at factory
MEASURES OF CENTER MODE • data value repeated most • seen as humps in a histogram 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
CALCULATING THE MEAN Pronounced “y-bar”
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 STANDARDDEVIATION • use with symmetric distribution RANGE • = max – min • good to mention for many distributions IQR • = Q3 – Q1 • use with skewed distribution • sometimes good to mention with symmetric distribution
CALCULATING STANDARD DEVIATION Variance: Standard Deviation:
