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DATA TABLES… KINDS OF VARIABLES… Qualitative vs. Quantitative Discrete vs. Continuous DISPLAYING a QUALITATIVE VARIABLE MORE about HISTOGRAMS
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DATA TABLE parties politics salary singer 5 mod. 80000 1.5 1 liberal
35000 3 2 40000 4
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VARIABLES CASES INDIVIDUALS whatever DATA TABLE Columns Rows parties
politics salary singer 5 mod. 80000 4.5 1 liberal 35000 3 2 40000 4 Rows CASES INDIVIDUALS whatever
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Kinds of Variables QUALITATIVE — Nominal — Just labels Ordinal — Order matters QUANTITATIVE — Discrete — Only certain values (for example, whole numbers) Continuous — Any value is possible (at least in some range)
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DISPLAYING ONE QUALITATIVE VARIABLE
Frequency table… Bar chart… Pie chart…
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Frequency table - politics
VALUE COUNT Liberal 20 Moderate 3 Conservative 2 TOTAL 25
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Frequency table - politics
VALUE COUNT PERCENT (of column) Liberal 20 80 % Moderate 3 12 % Conservative 2 8 % TOTAL 25 100%
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Frequency table – politics (Swarthmore)
VALUE COUNT PERCENT (of column) Liberal 46 64% Moderate 22 31% Conservative 4 6% TOTAL 72 100%
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Frequency table – singing
VALUE COUNT PERCENT 1 10 39 % 2 6 23 % 3 4 8 % 5 TOTAL 26 100 %
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Frequency table – singing
VALUE COUNT PERCENT 1 10 39 % 2 6 23 % 3 4 8 % 5 TOTAL 26 101 %
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Frequency table – singing
VALUE COUNT PERCENT 1 10 38 % 2 6 23 % 3 4 8 % 5 TOTAL 26 100 %
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Frequency table – singing (Swarthmore)
VALUE COUNT PERCENT 1 16 22% 2 3 23 32% 4 12 17% 5 7% TOTAL 72 100%
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EQUAL-AREA PRINCIPLE Areas are in proportion to data values.
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Salaries (Swarthmore)
600000 60000 50000 30000 very small 250000 75000 70000 80000 125000 35000 65000 200000 400000 72500 40000 150000 120000 20000 500000 45000 85000 90000 100000
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Salaries - $20,000 bin sizes
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$50,000 bin sizes
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$ bin sizes
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Constructing a histogram…
Define bins All the same size ? Easier if they are, but… Boundaries – ENDPOINT RULE Make a frequency table for your chosen bins… Construct histogram…
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Shape of a distribution…
Symmetrical ? Skew – right or left Unimodal Bimodal Multimodal Outliers
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