Chapter 2: Frequency Distributions - Yeatts

1 Chapter 2: Frequency DistributionsA table reporting the b f number of observations falling into each category of the Penalty Statutes 1993(data from which to create a Frequency distribution )StateMinimumAgeStateMinimum AgeArkansas14 Texas17 Virginia15 California18 Alabama16 Colorado18 Delaware16 Connecticut18 Indiana16 Illinois18 Kentucky16 Louisiana18 Source: Kathleen Maguire and Ann L. Pastore, eds., Sourcebook of Criminal Justice Statistics. 1994. Department of Justice, Bureau of Justice Statistics. Washington, : Government Printing Office, 1995, pp. Jersey18 Oklahoma16 New Mexico18 Wyoming16 Ohio18 Georgia17 Oregon18 New Hampshire17 Tennessee18 North Carolina17 Frequency11 Creating a Frequency DistributionMinimum AgeTally14|15|19412 Total N2715|16|||||||||17||||18||||||||||||NfP = Proportion (P): a relative Frequency obtained by dividing the Frequency in each category by the total number of cases.

2 Percentage (%):a relative f b i d b di idi Proportions and Percentagesfrequency obtained 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=Minimum Age Frequency Proportion Percentage1411/27=. and . Frequency DistributionMinimum Cumulative Age Freq. (f) (N) ** Doesn t total to 100% due to roundingMinimum Cumulative Age Frequency Percentage 5 Cumulative Percentage *Total ** Doesn t total to 100% due to roundingRatesA number obtained by dividing the number of actualoccurrences in a given time period by the number of rate, 1990 =Number of marriages in 1990ggTotal population in 1990 Marriage rate, 1990 = 2,448,000 marriages250,000,000 AmericansMarriage rate, 1990=.

3 0098( marriages for every 1000 people)Reading Statistical TablesBasic principles for understanding what the researcher is trying to tell you (that is, questions you should ask yourself when reading a table): What is the sourceof this table? How many variablesare presented? What are their names? What is represented by the numberspresented in the first column? In the second column?Example of Table Format for Research PaperTable 1: The Effect of Sex on Attitudes Toward the Death PenaltyIn Favor of the Death Penalty(actual number of respondents reported)YesNoTotalYesNoTotalMale361955 GenderFemale331851 Total6937106(Source: non-random sample obtained by students in a college statistics class)SPSS Output Looks Something Like This:V13 * V6 CrosstabulationV6Ye sN oTo t a l V13 MaleCount361955% within within Count331851% within within 6937106% within within V13 of Table Format for Research PaperTable 1.

4 The Effect of Sex on Attitudes Toward the Death PenaltyColumn %Percent In Favor of the Death Penalty*Row%YesNoTotal5251 Male6535100 Gender(36)(19)(55)4849 Female 6535100(33)(18)(51)Total100100100(69)(37 )(106)*Numbers in parentheses are actual numbers of respondentsChapter 4:Central TendencyCentral Tendency(mean, median, mode)The Mode: An Example Which of the three candidates represents the mode for these candidates Variable=Candidates Candidate A 11,769 votesCandidate B 39,443 votesCandidate C 78,331 votesLevel of measurement? =The Mode?=The Mode: An Example Which of the three candidates represents the mode for these candidates Variable=Candidates Candidate A 11,769 votesCandidate B 39,443 votesCandidate C 78,331 votesLevel of measurement =nominal (why?)

5 The Mode=Candidate C (why?)Finding Median Among Individual Cases# of hate crimes by stateCasesNC = 39 Penn = 141TX = 287 Ohio = 255 Fla= 240 Steps to Determine:1. Order the cases from highest to lowest or vice versa2. Add 1 to the total States ordered low to highNC=39 Penn=141 Fla=240 Ohio=255TX=287# of cases = 52. Add 1 to the total number of cases (5+1=6)3. divide resulting number 2 (6/2 = 3)4. Count down that many cases to identify the middle or median (Fla)Finding Median for a Frequency distributionI am very satisfied with my jobCummulativeValuesFreq FrequencySteps to Determine:1. divide total N by 2 to locate middle case: 28/2 = 14 Agree Strongly 5 5 Agree10 15 Undecided 3 18 Disagree 7 25 Dis.

6 Strongly 3 28 Total Cases: 282. determine cumulative frequencies3. locate the category that holds the middle case: agree contains the 14thcaseFormula for the MeanYfY = Y bar ( Y )equals the average or the sum of all the scores, Y, divided by the number of scores, the meanwith Frequency Distributions (grouped scores):Satisfaction with HealthFreq Categoryx Freq1 -Very High 5 5 Steps to Determine:1. multiply each category by its Frequency (category x Frequency )1 Very High 5 52 High 7 143 - Moderate 6 184 - Low 7 285 - Very Low 3 15 Totals: N=28; Freq=80 Frequency )2.

7 Sum all the category x freq scores to determine total (80)3. divide total (80) by total number of cases (total N or 28) to get average score ( ) NYfY =Considerations for Choosing a Measure of Central Tendency For a nominal variable, the modeis the only measure that can be used. For ordinal variables, the mode and the median For ord nal var ables, the mode and the med an may be used. The medianprovides more information (taking into account the ranking of categories). For interval-ratio variables, the mode, median, and mean may all be calculated. The meanprovides the most information about the distribution , but the median is preferred if the distribution is 5:The Importance of Measuring Variability Measures of Central Tendency -Numbers that describe what is typical or (t l) i di t ib ti ( average (central) in a distribution ( , mean, mode, median).)

8 Measures of Variability -Numbers that describe diversity or variability in the distribution ( , range, interquartile range, variance, standard deviation).The Range Range A measure of variation in interval-ratio variables. It is the difference between the highest (maximum) and the lowest (minimum) scores in the highest score - lowest scoreWhat is the range for these diversity scores?Steps to determine: subtract the lowest score ____from the highest _____to obtain the range of IQV IQV State IQV State IQVC alifornia Alabama Indiana New Mexico North Carolina Utah Texas Delaware Nebraska New (higher number means more diversity)?

9 New York Colorado South Dakota Oklahoma Wisconsin Maryland Connecticut Idaho New Jersey Arkansas Wyoming Louisiana Michigan Kentucky Arizona Tennessee Minnesota Florida Washington Montana Mississippi Massachusetts North Dakota Georgia Missouri Iowa Nevada Ohio West Virginia Illinois Pennsylvania New Hampshire South Carolina Kansas Maine Alaska Rhode Island Vermont Virginia Oregon What is the range for these diversity scores?

10 Steps to determine: subtract the lowest score the highest _____to obtain the range of IQV IQV State IQV State IQVC alifornia Alabama Indiana New Mexico North Carolina Utah Texas Delaware Nebraska New South (higher number means more diversity)?Hawaii Oklahoma Wisconsin Maryland Connecticut Idaho New Jersey Arkansas Wyoming Louisiana Michigan Kentucky Arizona Tennessee Minnesota Florida Washington Montana Mississippi Massachusetts North Dakota Georgia Missouri Iowa Nevada Ohio West Virginia Illinois Pennsylvania New Hampshire