# chapter3 - Chapter 3 Summarizing Data Graphical Methods 1...

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Chapter 3 Summarizing Data

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Graphical Methods - 1 Variable After data collected, sorted into categories/ranges of values so that each individual observation falls in exactly one category/range Numeric Responses : Break “range” of values into non- overlapping bins and count number of units in each bin Categorical Responses : List all possible categories (with “Other” if needed), and count numbers of units in each Pie Chart : Displays percent in each category/range Bar Chart : Displays frequency/percent per category Histogram : Displays frequency/percent per “range”
Constructing Pie Charts Select a small number of categories (say 5 or 6 at most) to avoid many narrow “slivers” If possible, arrange categories in ascending or descending order for categorical variables

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Philly Monthy Rainfall 1825-1869 (1/100 inches) 1 2 3 4 5 6 7 8 9 10 11 Category Range Count 1 <100 17 2 100-199 78 3 200-299 132 4 300-399 115 5 400-499 86 6 500-599 55 7 600-699 27 8 700-799 17 9 800-899 6 10 900-999 3 11 >1000 4 Monthly Philly Rainfall 1825-1869 (1/100 in)
Constructing Bar Charts Put frequencies on one axis (typically vertical, unless many categories) and categories on other Draw rectangles over categories with height=frequency Leave spaces between categories

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Constructing Histograms Used for numeric variables, so need Class Intervals Let Range = Largest - Smallest Measurement Break range into (say) 5-20 intervals depending on sample size Make the width of the subintervals a convenient unit, and make “break points” so that no observations fall on them Obtain Class Frequencies , the number in each subinterval Obtain Relative Frequencies , proportion in each subinterval Construct Histogram Draw bars over each subinterval with height representing class frequency or relative frequency (shape will be the same) Leave no space between bars to imply adjacency of class intervals
Histogram 0 20 40 60 80 100 120 140 100 300 500 700 900 1100 More rain100 Frequency 100 200 300 400 500 600 700 800 900 1000 1100 1200 More

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Interpreting Histograms Probability : Heights of bars over the class intervals are proportional to the “chances” an individual chosen at random would fall in the interval Unimodal : A histogram with a single major peak Bimodal : Histogram with two distinct peaks (often evidence of two distinct groups of units) Uniform : Interval heights are approximately equal Symmetric : Right and Left portions are same shape Right-Skewed : Right-hand side extends further Left-Skewed : Left-hand side extends further
Stem-and-Leaf Plots Simple, crude approach to obtaining shape of distribution without losing individual measurements to class intervals. Procedure:

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chapter3 - Chapter 3 Summarizing Data Graphical Methods 1...

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