Depicting Frequency Tables

• Qualitative (nominal or maybe ordinal) data– Histogram, bar charts and pareto charts– Pie chart

• Quantitative (interval or ratio, maybe ordinal) Data– Histograms and Bar Charts

• Absolute and relative frequency• Quickly spot distribution, trends and “hot-spots”

– Frequency Polygon– Ogive

• Cumulative frequency– Dotplots

• Frequency encoded in the vertical bar– Stem and Leaf Plots

Histogram Chart

• Bar lengths match frequency• Y axis can be frequency or relative frequency

02468

10121416

English

Langua

ges

Math

Misic a

nd ar

t PE

Scienc

e

Social S

tudie

s

Cou

nt

Pareto Chart

• Bar lengths match frequency• Y axis can be frequency or relative frequency• Bars ordered most to least, left to right

0%

5%

10%

15%

20%

25%

30%

PE

English

Social S

tudie

s

Misic a

nd ar

tMath

Scienc

e

Langua

ges

Coun

t

Live example

• Create a histogram of the favorite month

Your Turn

• Create a histogram of the favorite color

Pie Chart

• Wedges are proportional to the relative frequency

PEEnglishSocial StudiesMisic and artMathScienceLanguages

Creating a Pie Chart

• Create the relative frequency table• Calculate each wedge size:

– Multiply the relative frequency by 360• Use a compass and protractor to create the wedges• Use color and texture to differentiate wedges.

For example: PoE Class Demographics

Frosh 7Soph 5

Junior 3

Senior 10

Your Turn: CS Class Demographics

Frosh 2Soph 7

Junior 3

Senior 8

Pi Chart Example

Histogram

• Classes are represented as vertical bars on a graph– X axis are the class values– Ordered lowest to highest, left to right– Y axis is the frequency or relative frequency

• Length of bar is proportional to the number of counts in each class

• Color and texture differentiate bars from different data sets

• (On a bar chart, the bars are horizontal)

Histogram: August Temperatures

0

2

4

6

8

10

12

65 - 69 70 - 74 75 - 79 80 - 84 85 - 89

Cou

nt

20102010

Your Turn

• Create a histogram of Old Faithful Interval Data

Is this an accurate picture?

12%18%24%30%36%42%48%

Menendez Kean Undecided

Is this better?

0%20%40%60%80%

100%

Menendez Kean Undecided

Other Charts

• Frequency polygon– Class midpoint and frequency count are plotted on the

graph.– Dots are connected

• Ogive– Class midpoint and cumulative frequency are plotted on the

graph.– Dots are connected

Frequency Polygon

0

2

4

6

8

10

12

55 - 59 60 - 64 65 - 69 70 - 74 75 - 79 80 - 84 85 - 89

Ogive: August Temperatures

0

5

10

15

20

25

30

35

55 - 59 60 - 64 65 - 69 70 - 74 75 - 79 80 - 84 85 - 89

Stem and Leaf Plot

5

6 013788

7 123344446666779

8 0001112338

• Right column contains the set’s least significant digit• Left column contains the other digits

Homework

1. Draw a pareto chart of favorite color2. Draw a pie chart of gender3. Draw a pie chart of grade4. Draw a histogram of Math and CR SAT scores5. Draw a histogram of height6. Draw an Ogive chart of lucky number7. Draw a stem and leaf plot of height

Comparing Graphs

• Comparing the shape of two graphs

Histogram: August Temperatures

0

2

4

6

8

10

12

14

65 - 69 70 - 74 75 - 79 80 - 84 85 - 89

Coun

t

20082009

Frequency Polygon

0

2

4

6

8

10

12

14

16

18

60 - 64 65 - 69 70 - 74 75 - 79 80 - 84 85 - 89

2008

2008

Ogive: Old Faithful Intervals between Eruptions

0

5

10

15

20

25

30

35

60 - 64 65 - 69 70 - 74 75 - 79 80 - 84 85 - 89

2008

2009

Two Column Stem and Leaf Plot

5

578999 6 013788

01111222233445555556677 7 123344446666779

00 8 0001112338

• Left column contains the first set’s least significant digit

• Right column contains the second set’s least significant digit

• Center column contains the other digits