Descriptive Statistics. 2
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Questions and Answers

Why is it important to report the number of observations along with proportions and percentages?

  • It helps to impress readers with large numbers.
  • It allows readers to assess the adequacy of the sample size. (correct)
  • It guarantees that the results are universally applicable.
  • It reduces the need for statistical analysis.

    • What can be inferred if a report states, 'two out of three people questioned prefer courses in statistics' without mentioning the sample size?

  • The preference for statistics is uncommon.
  • The conclusion might be misleading due to a small sample. (correct)
  • The report is likely based on a large sample size.
  • The results are statistically significant.

    • Which formula should be used to calculate a proportion?

  • Divide f by n. (correct)
  • Subtract n from f.
  • Add f and n together.
  • Multiply f by n.

    • How is a percentage calculated from a proportion?

    <p>By multiplying the proportion by 100.</p> Signup and view all the answers

    Which statement is true about the values of f and n in a dataset?

    <p>f is usually smaller than n.</p> Signup and view all the answers

    What do ratios help to compare in a dataset?

    <p>The relative frequency of categories of a variable.</p> Signup and view all the answers

    What is the maximum value that a proportion can have?

    <p>1.00</p> Signup and view all the answers

    What does a percentage of 43% imply regarding the sample size when referring to gender?

    <p>43% of the sample consists of females out of the total sample size.</p> Signup and view all the answers

    What numerical code corresponds to individuals who identify as female?

    <p>2</p> Signup and view all the answers

    Which education level corresponds to the code 2?

    <p>Community college</p> Signup and view all the answers

    Which age group had the youngest participant in the sample?

    <p>23</p> Signup and view all the answers

    What does a score of 1 in the 'Support for Gun Control' variable indicate?

    <p>In favor of stricter gun laws</p> Signup and view all the answers

    How many different levels of education are represented by the numerical codes provided?

    <p>4</p> Signup and view all the answers

    What is the maximum age of participants in the provided cases?

    <p>77</p> Signup and view all the answers

    Which gender has the highest representation in the sample according to the cases provided?

    <p>Male</p> Signup and view all the answers

    What numerical code represents individuals who have less than a high school education?

    <p>0</p> Signup and view all the answers

    What is the benefit of increasing the interval width in a frequency distribution?

    <p>It allows for a more compact expression of data.</p> Signup and view all the answers

    Why are apparent gaps between intervals in a frequency distribution not problematic when age is measured in whole numbers?

    <p>No data points fall between the intervals.</p> Signup and view all the answers

    What happens when age is measured with greater precision, such as in tenths of a year?

    <p>It could create ambiguity in determining the interval for certain ages.</p> Signup and view all the answers

    What must be maintained to ensure mutual exclusivity between categories in a frequency distribution?

    <p>Gaps and appropriate precision in defining intervals.</p> Signup and view all the answers

    If ages were recorded in whole numbers, what would happen if intervals were defined without gaps?

    <p>Ambiguities in categorizing ages would arise.</p> Signup and view all the answers

    In the context of a frequency distribution, what defines an exhaustive and mutually exclusive set of intervals?

    <p>Set limits at consistent levels of measurement and include gaps.</p> Signup and view all the answers

    How could the limits of age intervals be expressed if age is measured in tenths of a year?

    <p>17.0–18.9</p> Signup and view all the answers

    What is a consequence of not properly defining interval limits in a frequency distribution?

    <p>Each case could fall into multiple intervals.</p> Signup and view all the answers

    What is the range of the given data set?

    <p>34</p> Signup and view all the answers

    Which interval represents the lowest scores in the frequency distribution?

    <p>2–4</p> Signup and view all the answers

    How many intervals should be used in the frequency distribution?

    <p>10</p> Signup and view all the answers

    What is the calculated interval size based on the range and number of intervals?

    <p>3</p> Signup and view all the answers

    What was the frequency of police response times of less than 6 minutes in 2000?

    <p>275</p> Signup and view all the answers

    Which time range saw the largest decrease in frequency from 2000 to 2020?

    <p>Less than 6 minutes</p> Signup and view all the answers

    What is the highest interval in the frequency distribution represented?

    <p>35–37</p> Signup and view all the answers

    What percentage of the total response times in 2020 fall into the '21 minutes or more' category?

    <p>5.0%</p> Signup and view all the answers

    How many cases fall within the interval of 14–16?

    <p>17</p> Signup and view all the answers

    What total number of students studied between 20 and 22 hours?

    <p>15</p> Signup and view all the answers

    How many people aged 40 or under reported having been in their mobile phone plan for 5 years?

    <p>5</p> Signup and view all the answers

    In the survey conducted by the telecommunications company, what is the cumulative percentage of responses for those over 40 with a plan duration of 2 years?

    <p>17%</p> Signup and view all the answers

    What should a researcher do if the frequency distribution table seems unsatisfactory?

    <p>Reconstruct it with different intervals</p> Signup and view all the answers

    What is the total frequency for police response times of 6–10 minutes in 2020?

    <p>350</p> Signup and view all the answers

    Which age group had the higher overall total in a surveyed mobile phone plan duration?

    <p>Over 40</p> Signup and view all the answers

    How many total responses were recorded in the year 2000 for police response times?

    <p>940</p> Signup and view all the answers

    What does the cumulative percentage column indicate about student study hours?

    <p>55.24% of students studied less than 20 hours.</p> Signup and view all the answers

    How many intervals are suggested as a reasonable convention when constructing frequency distributions?

    <p>10 to 15 intervals.</p> Signup and view all the answers

    Which step involves finding the range of scores?

    <p>Subtracting the low score from the high score.</p> Signup and view all the answers

    What is the recommended way to define interval limits?

    <p>Use the same level of precision as the data measurement.</p> Signup and view all the answers

    What should you do if the resultant frequency distribution has more than 15 intervals?

    <p>It should be simplified for better comprehension.</p> Signup and view all the answers

    What does the calculation of interval size involve?

    <p>Dividing the range by the number of intervals.</p> Signup and view all the answers

    How should frequencies be reported in a frequency distribution table?

    <p>Frequencies should be reported in a separate column labelled 'Frequency'.</p> Signup and view all the answers

    What percentage of students studied between 17 and 19 hours?

    <p>40.95%</p> Signup and view all the answers

    Study Notes

    Descriptive Statistics: Percentages, Ratios, and Rates

    • Percentages and Proportions: Percentages standardize raw data to a base of 100, while proportions standardize to 1.00. These tools are used to contextualize research findings and make comparisons more meaningful.

    • Proportion Formula: Proportion (p) = f/n, where 'f' is the frequency in a category and 'n' is the total number of cases.

    • Percentage Formula: Percentage (%) = (f/n) x 100%, where 'f' is the frequency in a category and 'n' is the total number of cases.

    Ratios

    • Ratio Definition: A ratio compares the relative frequency of two categories by dividing the frequency of one category by the frequency of another.

    • Ratio Formula: Ratio = f₁/f₂, where f₁ is the frequency of the first category and f₂ is the frequency of the second category.

    Rates

    • Rate Definition: A rate expresses the relative frequency of a phenomenon over time or a defined period. Rates are calculated by dividing the number of actual occurrences (factual) by the number of possible occurrences (fpossible) in a specific time period.

    • Rate Formula: Rate = factual / fpossible

    Frequency Distributions

    • Introduction: Frequency distributions summarize the distribution of variables by counting the number of cases in each category. They're useful for organizing and analyzing data.

    • Nominal Variables: Frequency distributions for nominal variables are straightforward: count occurrences in each category.

    • Ordinal Variables: Frequency distributions for ordinal variables are similar to nominal, but also include percentages which make the data more easily interpretable.

    Charts and Graphs

    • Pie Charts: Pie charts visually represent percentages. A circle is divided into proportionally sized segments, each representing a category's percentage.

    • Bar Charts: Bar charts use bars of constant width to represent frequencies. Bar charts are particularly useful for showing comparisons between categories.

    • Histograms: Histograms represent continuous data. Areas of bars correspond to the frequency of occurrence within a specified interval.

    Cumulative Frequency and Percentage

    • Cumulative Frequency: Shows the total number of cases below a particular score or range in an interval.

    • Cumulative Percentage: Represents the proportion of cases below a particular score or range.

    Interval-Ratio Variables

    • Construction: Frequency distributions for interval-ratio variables typically involve larger numbers of scores requiring intervals/data grouping.

    • Midpoints: For certain tasks, the midpoint between the upper and lower limits of an interval is helpful.

    • Real Limits: Real limits account for the possibility a value could fall between interval boundaries.

    ###Unequal Intervals

    • Reasons for unequal intervals: Some values are more densely clustered within the intervals (or are outside of typical interval ranges). Using different intervals, or open-ended intervals, can make the data more easily interpreted.

    SPSS Procedures

    • Frequency Distributions: Using SPSS, frequency distributions can be created and graphically visualized. The program provides cumulative frequency and percentage analysis.

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    PSCI 2702 Chapter 2 - Statistics PDF

    Description

    Test your knowledge about the importance of reporting observations, proportions, and percentages in statistics. This quiz will also cover key formulas and concepts related to ratios, sample size implications, and data analysis. Perfect for those looking to reinforce their understanding of statistical evaluation.

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