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CH-5 PPT - Displaying and Describing Quantitative Data...

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Displaying and Describing Quantitative Data
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Displaying and Describing Quantitative Data Summarizing numerical data Histograms Stem-and-Leaf plots Shape and Skewness Center: Mean vs. Median
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Continuous Data: may take on any value in some interval Summarized in a grouped data frequency table Example: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature 24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27 NOTE: Temperature is a continuous variable because it could be measured to any degree of precision desired Frequency Distribution: Continuous Data
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1. Determine the number of categories (classes/bins) 2. Establish class width Minimum width is the range of the data Largest data point – Smallest data point = Range 3. Set the class boundaries 4. Determine the frequency in each class Count the number of data points in each category Building a Frequency Table: Continuous Data
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How Many Categories? Many (Narrow class intervals ) May yield a very jagged distribution with gaps from empty classes Can give a poor indication of how frequency varies across classes Few (Wide class intervals ) May compress variation too much and yield a blocky distribution Can obscure important patterns of variation 0 2 4 6 8 10 12 0 30 60 More Temperature Frequency 0 0.5 1 1.5 2 2.5 3 3.5 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 More Temperature Frequency (X axis labels are upper class endpoints)
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General Guidelines Number of Data Points Number of Classes under 50 5 - 7 50 – 100 6 - 10 100 – 250 7 - 12 over 250 10 - 20 Class widths can typically be reduced as the number of observations increases Distributions with numerous observations are more likely to be smooth and have gaps filled since data are plentiful
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Considerations: Continuous Data Must be mutually exclusive Must be all-inclusive Bins should be of equal width Avoid empty categories
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How should the endpoints be determined?
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