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)