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    Chapter 2: Organization of

    Information:

    Frequency Distributions Frequency Distributions Proportions and Percentages Percentage Distributions

    Comparisons The Construction of Frequency Distributions

    Frequency Distributions for Nominal Variables Frequency Distributions for Ordinal Variables Frequency Distributions for Interval-Ratio Variables

    Cumulative Distributions Rates Reading the Research Literature

    Basic Principles Tables with a Different Format

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    Frequency Distributions

    A table reporting the number of observationsfalling into each category of the variable.

    Identity Frequency (f)

    Native American 947,500

    Native American of multiple ancestry 269,700

    Native American of Indian descent 5,537,600Total (N) 6,754,800

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    Death Penalty Statutes

    In 1993, 36 states and Washington, D.C. had

    statutes permitting capital punishment. Of these

    36 states, 27 set a minimum age for execution.

    Assume you are a member of a legal reformgroup that is trying to get the states that do not

    have a minimum age for execution to change

    their laws. You want to prepare a report

    describing the minimum age for execution in the

    27 states have an established minimum age for

    execution. (The data are on the following slides.)

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    Death Penalty Statutes

    Source: Kathleen Maguire and Ann L. Pastore, eds., Sourcebook of Criminal JusticeStatistics. 1994. U.S. Department of Justice, Bureau of Justice Statistics. Washington,D.C.: U.S. Government Printing Office, 1995, pp. 115-116.

    StateMinimum

    Age StateMinimum

    Age

    Arkansas 14 Texas 17

    Virginia 15 California 18

    Alabama 16 Colorado 18

    Delaware 16 Connecticut 18

    Indiana 16 Illinois 18

    Kentucky 16 Louisiana 18Mississippi 16 Maryland 18

    Missouri 16 Nebraska 18

    Nevada 16 New Jersey 18

    Oklahoma 16 New Mexico 18

    Wyoming 16 Ohio 18

    Georgia 17 Oregon 18New Hampshire 17 Tennessee 18

    North Carolina 17

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    Frequency

    1

    1

    9

    4

    12

    Total N 27

    Creating a Frequency Distribution

    Minimum Age Tally

    14 |

    15 |

    16 |||||||||

    17 ||||

    18 ||||||||||||

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    Creating a Frequency Distribution

    Minimum Age Frequency

    14 1

    15 1

    16 9

    17 4

    18 12

    Total N 27

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    N

    fP

    Proportion (P):a relative frequencyobtained by dividing the frequency in

    each category by the total number of

    cases.

    Percentage (%):a relative frequencyobtained by dividing the frequency in

    each category by the total number of

    cases and multiplying by 100.

    N:total number of cases

    Proportions and percentages are

    relative frequencies

    )100((%) P

    Proportions and Percentages

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    Minimum Age Frequency Proportion Percentage

    14 1 1/27=.037 3.7

    15 1 .037 3.716 9 .333 33.3

    17 4 .148 14.8

    18 12 .444 44.4Total N 27 1.0 100.0

    Proportions and Percentages

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    PercentageDistributions

    A table showing the percentage of observationsfalling into each category of the variable.

    Minimum

    Age Frequency Percentage4 1 3.7

    15 1 3.7

    16 9 33.3

    17 4 14.8

    18 12 44.4

    Total N 27 100.0

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    Frequency Distributions for

    Nominal VariablesGender Tallies Freq. (f) Percentage

    Male ||||||||||||||| 15 37.5

    Female ||||||||||||||||||||||||| 25 62.5

    Total (N) 40 100.0

    Note: The categories for nominal variables (male,female) need not be listed in any particularorder.

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    Frequency Distributions for

    Ordinal VariablesHappiness Tallies Freq. (f) Percentage

    Very Happy ||||||||| 9 22.5

    Pretty Happy ||||||||||||||||||||||||| 25 62.5Not too happy |||||| 6 15.0

    Total (N) 40 100.0

    Note: Because the categories or values of ordinal variables are rank-ordered, they must be listed in a way that reflects their rankfrom the lowest to the highest or from the highest to thelowest.

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    Employment Status Example

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    Employment Status Example

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    Frequency Distributions for

    Interval-Ratio Variables

    Number of Children Freq. (f) Percentage

    0 5 12.5

    1 10 25.0

    2 10 25.0

    3 5 12.5

    4 5 12.5

    5 1 2.56 2 5.0

    7 or more 2 5.0Total (N) 40 100.0

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    Cumulative Distributions

    Sometimes we are interested in locating therelative position of a given score in a distribution.

    Cumulativefrequency distribution:adistribution showing the frequency at or beloweach category (class interval or score) of thevariable.

    Cumulativepercentage distribution:adistribution showing the percentage at or beloweach category (class interval or score) of thevariable.

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    Cumulative Frequency

    Distribution

    Minimum Cumulative

    Age Freq. (f) Percentage Frequency

    14 1 3.7 1

    15 1 3.7 2

    16 9 33.3 11

    17 4 14.8 15

    18 12 44.4 27Total (N) 27 100.0

    * Doesnt total to 100% due to rounding

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    Minimum Cumulative

    Age Frequency Percentage Percentage

    14 1 3.7 3.7

    15 1 3.7 7.416 9 33.3 40.7

    17 4 14.8 55.5

    18 12 44.4 99.9*Total N 27 100.0

    * Does not total to 100% due to rounding

    Cumulative Percentage Distribution

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    RatesA number obtained by dividing the number of

    actualoccurrences in a given time period by thenumber ofpossible occurrences.

    Whats the problem with the ratecomputation below?

    Marriage rate, 1990 = Number of marriages in 1990

    Total population in 1990

    Marriage rate, 1990 = 2,448,000 marriages250,000,000 Americans

    Marriage rate, 1990 = .0098

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    Reading Statistical Tables

    Basic principles for understanding what theresearcher is trying to tell you:

    What is the source of the table? How many variables are presented? What

    are their names?

    What is represented by the numberspresented in the first column? In the secondcolumn?