2314 Review Part I - QMBE 2786 Intermediate Statistics for...

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QMBE 2786 Intermediate Statistics for Business and Economics A Business-Related Review of Elementary Statistics ( UNO Math 2314) (A previous course in statistics is normally considered a mandatory prerequisite.) 1. Data categories, etc. Data Categories elements -- entities on which data is collected variable -- an element characteristic of interest observation -- a set of measurements for a particular element (see table 1.1, p. 5) Measurement scales nominal -- variable is a label or name ordinal -- variable has nominal properties, but rank is meaningful interval -- rank is meaningful and the interval between values can be expressed in a unit of measure. Interval data is always numeric. ratio -- interval data for which the ratio of two values is meaningful. Always numeric. Must have a zero value. Qualitative data is either nominal or ordinal and may be numeric or non-numeric. Quantitative data may use either an interval or ratio scale of measurement and is always numeric. Whether a particular kind of statistical analysis is appropriate will depend on the type of variable(s) involved. Exercises: 1. A possible source of data is company employee records. Some of the available data may be: Name, address, s.s.#, number of sick days, salary, minority status, etc. Discuss these sorts of data in light of the above categories. 2. Into what category of measurement scale does the variable " temperature Celsius" fall? 3. American universities are often rated by their "party school" status. Last year Tulane ranked 10th. What kind of measurement scale is this? 4. A questionnaire asks your religion. What kind of data is this? 5. Give an example of data that is nominal but not ordinal, ordinal but not interval, etc. 2. Descriptive Statistics. Given a set of numbers, whether we regard it as a population or as a sample selected from a population, there are certain commonsensical descriptive procedures ( summaries) we can apply. So what, by way of description, can you do with a set of numbers? 1. Improve the coherence of the data by organizing it into frequency and relative frequency ( also percent frequency) distribution tables. The mechanics of this procedure: a) Pick the number of frequency classes so that coherence is actually improved. This depends on the size and the nature of the data set, but
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a rough rule is to use 5 to 20 classes. Review p. 2 b) Choose the classes, that is, set numerical values ( for quantitative data) that define the classes. These are called the class limits. Do this in such a way that each item falls into one and only one class and, preferably, all the classes are the same width. 2. Make pictures or graphs that at a glance reveal the trends within the data set. There are many possibilities: bar graphs, histograms ( a special sort of bar graph), ogives, frequency polygons, pie charts, etc. If you don't have a better hobby, you can spend hours with the Excel Chart Wizard. From a purely mathematical point of view, the most important of these is the relative frequency histogram. 3. Compute various items of summary arithmetic. These are also called
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2314 Review Part I - QMBE 2786 Intermediate Statistics for...

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