1

http://www.ccs.neu.edu/home/amislove/twittermood/

Blue Green Yellow Orange Red

Very Safe Very Unsafe

Mapping Super Storm Sandy Experience

2

Organizing Data: Frequency

Distributions

• Organized tabulation of the individual scores

located in each category on the scale of

measurement

• Allows a quick picture of all the scores.

• Are the scores generally high or low?

• Are the scores concentrated in one area or are

they spread out across the entire scale?

• Can see the location of a specific individual

score relative to all other scores

Organizing Data: Frequency

distributions

• Can be structured as a table or as a graph

• Need the categories that make up the

original scale

• Need the frequency (number of

individuals) of each score

3

Basic math: Proportions: Fractions,

Decimals, and Percentages

• A proportion is a part of a whole and can be expressed as a fraction, decimal or a percentage.

40 students 3 fail

Proportion = 3/40

Decimal = .075

Percentage=7.5%

Basic math: Proportions: Fractions,

Decimals, and Percentages

Fraction 1

10

1

4

1

2

3

4

Decimal 0.10 .25 .50 .75

Percentage 10% 25% 50% 75%

4

Frequency distribution: table

Test Scores

80 80

90 70

80 80

70 100

100 90

90 80

60 60

40 90

90 70

80 80

Place

lowest

to

highest

Frequency distribution: table

Test Scores

80 80

90 70

80 80

70 100

100 90

90 80

60 60

40 90

90 70

80 80

Place

lowest

to

highest

X f

40 1

60 2

70 3

80 7

90 5

100 2

f

The number of times each value appears

5

Relative frequency of a score (rf):

The frequency of a score divided by the total

number of scores obtained

X f f of a score/N rf

40 1 1/20= .05

60 2 2/20= .10

70 3 3/20= .15

80 7 7/20= .35

90 5 5/20= .25

100 2 2/20= .10

N=20

Rf of a score = f of a score/N

Percentage frequency (%f ):

The relative frequency of a score multiplied

by 100

X f f of a score/N rf (%f of a score × 100)

40 1 1/20= .05 5%

60 2 2/20= .10 10%

70 3 3/20= .15 15%

80 7 7/20= .35 35%

90 5 5/20= .25 25%

100 2 2/20= .10 10%

N=20

% f of a score = rf of a score × 100

6

Cumulative frequency (cf ):

The frequency of occurrence of that score plus the sum of

the frequencies of all the scores of lower value

X f cf crf c%f

40 1 1 1/20=.05 5%

60 2 3 3/20=.15 15

70 3 6 6/20=.30 30

80 7 13 13/20=.65 65

90 5 18 18/20=.90 90

100 2 20 20/20=1.00 100

N=20

Ungrouped frequency distribution

table

X f %f cf %cf

40 1 5 1 5

60 2 10 3 15

70 3 15 6 30

80 7 35 13 65

90 5 25 18 90

100 2 10 20 100

N=20

7

Grouped frequency distributions

• A frequency distribution in which scores

are grouped together in class intervals and

the frequency of scores occurring within

each class is tabulated

• Used when have large range of values

Grouped frequency distribution

tables

• Rule 1: Number of Class Intervals should be around 10.

• Rule 2: Width should be a relatively simple number: 2, 5, 10 or 20.

• Finding class intervals

Rows = highest – lowest

94-53=41

• Test scores: 82, 75,

88, 93, 53, 84, 87, 58,

72, 94, 69, 84, 61, 91,

64, 87, 84, 70, 76, 89,

75, 80, 73, 78, 60

8

Grouped frequency distribution

tables

• Constructing class

intervals

• Test scores: 82, 75,

88, 93, 53, 84, 87, 58,

72, 94, 69, 84, 61, 91,

64, 87, 84, 70, 76, 89,

75, 80, 73, 78, 60

X f

50-54 1

55-59 1

60-64 3

65-69 1

70-74 3

75-79 4

80-84 5

85-89 4

90-94 3

test

Test

9

Similar to frequency tables, but also provide a visual depiction of the frequency of each score.

•They are created by listing all of the data from highest to lowest score.

•The left column is the first digit of a score and the right column contains every subsequent digit of all scores that start with the first digit.

Stem and Leaf Displays:

TEXTANX Stem-and-Leaf Plot

Frequency Stem & Leaf

2.00 2 . 19

3.00 3 . 278

3.00 4 . 047

4.00 5 . 1799

4.00 6 . 1349

Stem width: 10.00

Each leaf: 1 case(s)

A picture is worth a thousand words

Graphs: Histogram

1. make frequency table (or grouped frequency) 8,7,4,10,8,6,8,9,9,7,3,7,6,5,0,9,10,7,7,5,2,1,6,7,10,8,8,

Life satisfaction f %

10 3 10

9 3 10

8 5 16.7

7 7 23.3

6 4 13.3

5 2 6.7

4 1 3.3

3 2 6.7

2 1 3.3

1 1 3.3

0 1 3.3

10

2. Put the values along the bottom

of the graph

3. Make a scale of frequencies

along the left edge of graph that

starts at 0 at the bottom to the

highest possible frequency for

any value

• Make a bar above each value

with a height of frequency

7

9

8

7

6

5

4

3

2

1

0

0 1 2 3 4 5 6 7 8 9 10

Grouped frequency

histogram

Life satisfaction f

10-11 3

8-9 8

6-7 11

4-5 3

2-3 3 0-1 2

The widths of the

rectangles represent

class intervals and

heights represent

corresponding

frequencies

11

Organizing data: Graphs

• Bar graph

• Histograms

• Line Graphs

Bar Graphs

• For Nominal or Ordianal Data

MAR SEP DIV WID

MARITAL STATUS of PARENTS

0

30

60

90

120

150

Fre

qu

en

cy

12

0 20 40 60 80 100

Alcohol

Cigarettes

Marijuana

Smokeless tobacco

Ampetamines

Inhalants

LSD

Cocaine

Barbituates

Ecstasy

Heri\oin

Example of a Bar Chart % of high school seniors who have

ever used drugs

Johnston & al., 1999

Example of a Bar Chart: % of High School

Students Who Ever Had Sexual Intercourse

* B, H > W; B > H

National Youth Risk Behavior Survey, 2003

48.0

41.8

67.3

51.4

45.346.7

0

20

40

60

80

100

Total Female Male White Black* Hispanic*

Perc

en

t

13

Organizing data: Graphs

• Histogram: interval or ratio

15.00 20.00 25.00 30.00 35.00

affect

0

1

2

3

4

5

Fre

qu

en

cy

Mean = 23.56Std. Dev. = 6.58331N = 25

20.00 30.00 40.00 50.00 60.00 70.00

taitot

0

1

2

3

4

5

6

7

Fre

qu

en

cy

Mean = 42.74Std. Dev. = 12.62696N = 25

Organizing data: Graphs

• Frequency polygon: Ordinal, interval, or

ratio Note: In SPSS have options

what the line represents.

The options include n of

cases, cumulative n of

cases, % of cases and

cumulative % of cases. On

this graph, it is the number

of cases for each score that

is plotted

14

Organizing data: Graphs

On this graph,

it is each

person’s score

that is plotted

* In a car or other vehicle one or more times during the 30 days preceding the survey 1 Significant linear decrease, p < .05

National Youth Risk Behavior Surveys, 1991 - 2003

Example of a Frequency Polygon/line graph. This chart

illustrate the percentage of high school students drinking

and driving in 1991 through 2003

16.713.5 15.4 16.9

13.1 13.3 12.11

0

20

40

60

80

100

1991 1993 1995 1997 1999 2001 2003

Perc

en

t

Note: On this graph, it is the

percentage cases in this

case high school students

that is plotted

15

Shapes of Distributions

• Unimodal Distribution

10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

grades

0

5

10

15

20

25

Co

un

t

Shapes of Distributions

• Bimodal Distribution

10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

grades

2

4

6

8

10

12

14

Co

un

t

16

Shapes of Distributions

• Rectangular Distribution

1.00 2.00 3.00 4.00

grade level

0

5

10

15

20

Num

ber

of s

tude

nts

Symetrical Distibution

Approximately equal

number of scores on

both sides

0.00 20.00 40.00 60.00 80.00 100.00 120.00

happiness

0

5

10

15

20

Fre

qu

ency

Self-reported general happiness in a sample of young adults

17

Positively Skewed Distribution

0.00 30.00 60.00 90.00 120.00 150.00

happiness

0

2

4

6

8

Freq

uenc

ySelf-reported general happiness among sample of senior

citizens

Direction of the tail

tells you that it is a

positive skew which

means scores are

towards the end of

the distribution

•more low scores than high scores

Negatively Skewed Distribution

0.00 30.00 60.00 90.00 120.00 150.00

happiness

0

2

4

6

8

10

Freq

uenc

y

Self-reported general happiness in sample of college studentsDirection of the tail

tells you that it is a

negative skew

which means

scores are towards

the front of the

distribution.

more high

scores

than low

scores

18

Shape of the Distribution: Kurtosis flatness or ’peakedness’

Mesokurtic

0.00 30.00 60.00 90.00 120.00 150.00

self-esteem

0

10

20

30

40

50

Fre

qu

en

cy

If the curve is more

peaked than a normal

curve means that the

scores are clustered

around the mode (the

most frequently

occurring score).

Leptokurtic

0.00 20.00 40.00 60.00 80.00 100.00

self-esteem

0

2

4

6

8

10

12

Fre

qu

en

cy

If the curve is more flat

means that the scores

are more spread out

Platykurtic

0.00 20.00 40.00 60.00 80.00 100.00 120.00

self-esteem

0

5

10

15

20

Fre

qu

en

cy