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Chapter 2

# Stats 1 - Chapter 2.docx

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Stats I - Chapter 2 – Descriptive Techniques I Descriptive statistic involves - Arranging - Summarizing - Presenting A set of data in such a way that useful information is produced Its methods make use of graphical techniques and numerical descriptive measures (such as averages) to summarize and present the data. A variable is some characteristic of a population or sample. - E.g. student grades. - Typically denoted with a capital letter: X, Y, Z… The values of the variable are the range of possible values for a variable. - E.g. student marks (0..100) Data are the observed values of a variable. - E.g. student marks: {67, 74, 71, 83, 93, 55, 48} Interval data - Real numbers, i.e. heights, weights, prices, etc. - Also referred to as quantitative or numerical. - Arithmetic operations can be performed on Interval Data, thus its meaningful to talk about 2 x Height, or Price + \$1, and so on. Nominal data - The values of nominal data are categories of the data collected: - E.g. responses to questions about marital status, coded as: Single = 1, Married = 2, Divorced = 3, Widowed = 4 - 30 M and 45 F or 30 B and 45 G = Coding of nominal data - Nominal data are only counts These data are categorical in nature; arithmetic operations don’t make any sense (e.g. does Widowed ÷ 2 = Married?!) Nominal data are also called qualitative or categorical Ordinal Data - appear to be categorical in nature, but their values have an order; a ranking to them: E.g. College course rating system: poor = 1, fair = 2, good = 3, very good = 4, excellent = 5 While it is still not meaningful to do arithmetic on this data (e.g. does 2*fair = very good?!), we can say things like: Excellent > poor OR fair < very good Excellent greater than poor OR fair less than very good That is, order is maintained no matter what numeric values are assigned to each category. As mentioned above, - All calculations are permitted on interval data. - Only calculations involving a ranking process are allowed for ordinal data. - No calculations are allowed for nominal data, save counting the number of observations in each category. This lends itself to the following “hierarchy of data”… Hierarchy of Data Interval - Values are real numbers. - All calculations are valid. - Data may be treated as ordinal or nominal. Ordinal - Values must represent the ranked order of the data. - Calculations based on an ordering process are valid. - Data may be treated as nominal but not as interval. Nominal - Values are the arbitrary numbers that represent categories. - Only calculations based on the f
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