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Basic Descriptive Statistics

Learn about percentages, proportions, ratios, rates, frequency distributions, and graphing techniques to interpret and present statistical data effectively.

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Basic Descriptive Statistics

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  1. Basic Descriptive Statistics • Percentages and Proportions • Ratios and Rates • Frequency Distributions: An Introduction • Frequency Distributions for Variables Measured at the Nominal and Ordinal Levels

  2. Basic Descriptive Statistics (cont) • Frequency Distributions for Variables Measured at the Internal Ratio Levels • Constructing Frequency Distributions for Interval-ratio Level Variables • Charts and Graphs • Interpreting Statistics: Analyze Changing Patterns of Workplace Surveillance

  3. PercentageThe number of cases in a category of a variable divided by the number of cases in all categories on the variable, the entire quantity multiplied by 100. • ProportionThe number of cases in one category of a variable divided by the number of cases in all categories of the variable.

  4. ratiosThe number of cases in one category divided by the number of cases in some other category. • rateThe number of actual occurrences of some phenomena or trait divided by the number of possible occurrences per some unit of time.

  5. frequency distributionsTables that summarize the distribution of a variable by reporting the number of cases contained in each category of the variables. • class intervalsCategories used in the frequency distributions for interval-ratio variables.

  6. midpointsThe points exactly halfway between the upper and lower limits, found by dividing the sum of the upper and lower limits by two. • cumulative frequencyAn optional column in a frequency distribution that displays the number of cases within an interval and all preceding intervals.

  7. cumulative percentageAn optional column in a frequency distribution that displays the percentage of cases within an interval and all preceding intervals. • pie chartsA graphic display device especially for discrete variables with only a few categories.

  8. bar chartsA graphic display device for discrete variables. • histogramA graphic display device for interval-ratio variables. Class intervals are represented by contiguous bars of equal width, the height of each corresponding to the number of cases in the interval.

  9. line chartsA graphic display device for interval-ratio variables. Class intervals are represented by dots placed over the midpoint, the height of each corresponding to the number of cases in the interval. All dots are connected by straight lies. • graphic display device for interval-ratio variables. Class intervals are represented by dots placed over the midpoint, the height of each corresponding to the number of cases in the interval. All dots are connected by straight lies.

  10. Deciding on a Descriptive Format • How to present the data. • What kind of information to lose. • How much detail can safely be obscured.

  11. Guidelines for Using Percentages and Proportions • When working with a small number of cases, report the actual frequencies rather than percentages of proportions. • Always report the number of observations along with proportions and percentages. • Proportions and percentages can be calculated at any level of measurement.

  12. Graphing Techniques:Discrete Variables • Pie charts • Bar charts

  13. Graphing Techniques:Interval-ratio Variables • Histogram • Line charts

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