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Understanding Percentages, Proportions, Rates of Change, and Frequency Distributions

This lecture focuses on key statistical concepts: percentages, proportions, rates of change, and frequency distributions. We define proportions as the ratio of cases in one category versus all cases, while rates express this with a base of 100. Percentage change quantifies how much a variable has shifted over time. Frequency distributions summarize data distributions by detailing case counts in each category. Utilizing SPSS for constructing frequency tables, we explore grouping data, calculating ranges, setting group limits, and counting cases. Ideal for students seeking to strengthen their statistical knowledge.

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Understanding Percentages, Proportions, Rates of Change, and Frequency Distributions

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  1. SP 225Lecture 5 Percentages, Proportions, Rates of Change and Frequency Distributions

  2. Proportion • The number of cases in one category of a variable divided by the number of cases in all categories of a variable

  3. Rates • Definition: A proportion written with a base other than 1

  4. Percentage • Definition: a rate written with a base of 100

  5. Percentage Change • Definition: A statistic that tells how much a variable has changed over time.

  6. Frequency Distribution Definition: A table that summarizes the distribution of a variable by reporting the number of cases contained in each of its categories

  7. Frequency Distribution

  8. Frequency Distribution with Percentages

  9. Frequency Distribution with Cumulative Frequency

  10. Frequency Distribution with Cumulative Percentages

  11. Frequency Tables SPSS

  12. Making Decisions Based on Ordinal Data • Cannot truly calculate an average score • Cannot directly compare categories

  13. Frequency Tables for Interval/Ratio Data • Group categories • Groups represent ranges of values

  14. Constructing a Frequency Table • Decide upon a number of groups • Find the range of data by subtracting the minimum value from the maximum value • Divide the range by the number of groups to get the minimum group size • Define the lower limit of the lower interval and begin building the groupings • Count the number of cases in each group

  15. Example Frequency Table 5 10 17 13 8 12 19 22 15 3 9 2 14 16 20 19 18 7 14 23 14 21 28 18

  16. Constructing a Frequency Table in SPSS • Use recode command to group data • Groups must be created manually before frequency table is constructed

  17. Reading For Next Class • No Additional Reading

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