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Frequency and Tally
•What is Tally and how to do it?
Previous Arrest of 10 Known Offenders
Offender 1: 0 Offender 6: 7
Offender 2: 0 Offender 7: 2
Offender 3: 0 Offender 8: 2
Offender 4: 3 Offender 9: 7
Offender 5: 5 Offender 10: 4
Frequency and Tally
Previous Arrest No. of Offenders0 / / /12 / /3 /4 /5 /67 / /
Tallying cases. A frequency distribution. All you do is count!
Percentage Distribution: Percent
• Why we need percentage distributions?• How to calculate percentage distribution?
Two steps1. Divide each frequency by the total number of cases2. Multiply that result by 100
Percent = f/N*100
F=frequency
N=Total Number of cases
Percent = f/N*100
F=frequency
N=Total Number of cases
Percentage Distribution: Proportion
• What are the differences between proportion and percent?
• What is the result of sum-up of a set of percent?
• What is the result of sum-up of a set of proportion?
• When we are given a total number of cases, a percent, can we obtain the corresponding frequency?
Proportion=f/N
f: frequency
N: total number of cases
Proportion=f/N
f: frequency
N: total number of cases
In-class Exercise 1
Previous arrest Frequency Percent Proportion0 31 02 23 14 15 16 07 2
Total (N)
In-class Exercise 2
A Civil Disobedience Survey
Civil Disobedience Frequency PercentProportion
• Follow Conscience 55
• Obey Law 78
Total N=
In-class Exercise 3
A survey of death penalty on (N=467) inmates in China
• 85% committed murder• 7% committed rape • The rest committed terrorist crimes• How many murderers are on death toll?• How many rapists are on death toll?• How many terrorist criminals are on death toll?
In-class Exercise 4
Survey of 15 individuals of their educations (LS: Below high school; HS: high school; C: college; G: graduate;)
1: HS 6: C 11: G2: HS 7: C 12: G3: LS 8: C 13: LS4: C 9: G 14: HS5: C 10: C 15: C
Exercise 4 continues
• Arkansas had about 2.5 million residents. If our sample is a good representation of Arkansas education level, how many people in Arkansas have college education?
• Minnesota has about 5 million people, if it is a good representation for Minnesota education level, how many people in Minnesota have high school education?
Cumulative Distributions
A cumulative percentage is the percentage of all scores that have a given value or less. To obtain a cumulative percentage
1. Add all frequencies for the given value and all lesser values2. Divide that sum by the total number of cases3. Multiply that result by 100
Education Attainment Frequency Percent Cumulative PercentBelow (0 - 8 years) 17 22High school (9 – 11 years) 34 44College (12 – 14 years) 19 24Graduate (15 years +) 8 10Total (N) 78
Usage of Cumulative Percentage
• Differences between percentage and cumulative percentage.
• Use of Cumulative percentage in nominal variable?
Population Percent Cumulative Percent?
East Coast 34 --
West Coast 45 --
Midwest 5 --
Mideast 7 --
South 9 --
Creating Tables
• Rounding-off• Creating presentation-quality tables
1. Decimal places consistent
2. Categories mutually exclusive and collectively exhaustive
3. Descriptive names
4. No vertical lines
5. And many more on page 39-40
In-class Exercise 5
Round-off the following numbers to one-decimal place
1. 34.23
2. 45.31
3. 56.45
4. 89.97
5. 73.56
6. 81.75
Review
• Raw data• Tallying• Frequency• Proportion• Percent• Cumulative percent• Rounding-off• Good table presentation
Example 1
1995 Hate Crime By RaceRace No. of Offenders
White 4,991
Black 2,253
American Indian/Alaskan Native 45
Asian/Pacific Islander 211
Multi-Racial 318
Unkown 615
Total (N) 8,433
Source: FBI on-line document (http://www.fbi.gov/ucr/hatecm.htm)
General Social Survey (GSS)
The GSS (General Social Survey) is an almost annual "omnibus," personal interview survey of U.S. households conducted by the National Opinion Research Center (NORC)
• Annual Survey 1972 – 2000, except 1979, 1981, 1992• Topics Very General• Questions replication• Cross-national comparison• High survey standard• Very important databases for social science studies
Example 2
1998 General Social Survey
“Would you allow racists to speak?”
Frequency Percent
Yes 1173 63.8
No 665 36.2
Total (N) 1838
Pie Presentation
NOT ALLOWED
ALLOWED
Example 3
1998 General Social Survey
“How happy are you with your marriage?”
Frequency Percent
Very Happy 855 63.9
Pretty Happy445 33.3
Not Too Happy 37 3.8
Total (N) 1337
Bar Chart
HAPPINESS OF MARRIAGE
NOT TOO HAPPYPRETTY HAPPYVERY HAPPY
Pe
rce
nt
70
60
50
40
30
20
10
0
Exercise 6
General Social Survey 1991“On the whole, how satisfied are you with the work-would you say very
satisfied, moderately satisfied, a little dissatisfied, or very dissatisfied?”Frequency Percent Cumulative
PercentVery satisfied 510Moderately satisfied 482A little dissatisfied 108Very dissatisfied 49 Total (N)
Exercise 7
1998 General Social Survey“God watches over me.”Response Frequency PercentStrong agree 833 58.9Agree 426 30.1Disagree 105 7.4Strongly disagree 51 3.6Total (N) 1415 100
Exercise 7 continues
1998 General Social Survey
“Have you seen an X-rated movie in the last year?” (All Respondents)
Response Frequency Percent
Yes 452
No 1444
Missing 936
Total (N) 2832
Exercise 7 continues
1998 General Social Survey
“Have you seen an X-rated movie in the last year?” (Those who strongly believe that God is watching over them)
Response Frequency Percent
Yes 117
No 435
Missing 281
Total (N) 833
Exercise 8
1998 General Social SurveySchooling Frequency Percent Cumulative Percent
0-4 14
5-9 69
10-14 516
15-19 177
20 + 16
Total (N)