Displaying Categorical Data
CH. 3 Day 1 NotesAP Statistics
EQ: How do we display categorical data?
Warm UpIdentify the W’s, name the variables and
specify if it should be treated as categorical or quantitative.
A listing posted by the Arby’s restaurant chain gives, for each of the sandwiches it
sells, the type of meat in the sandwich, the number of calories, and the serving size in ounces. The data might be used to assess
the nutritional value of the different sandwiches.
Warm Up - Answer• Who (are we studying): Arby’s
sandwiches• What (characteristics are we using): oType of meat (categorical)onumber of calories (quantitative)
(calories)oserving size (quantitative) (ounces)
• When: Not specified• Where: Arby’s restaurants• How: We are using the list posted by the
restaurant
Tell whether the variable is categorical, quantitative, or an identifier.
1.Shoe size2.VIN number of a car3.Number of pages in a book4.Class rank5.Length of your arm
QI
QI or C
Q
ExtraIn what way might Age be
considered to be a quantitative variable?
What about as a categorical variable?
Ways to Represent Data
Today we will focus on:
Frequency Tables
RelativeFrequency
Tables
Bar ChartsBar Charts
Pie Charts
Frequency Tables• Helps organize data• Records totals and categories• Relative frequency table-displays
the percentages(proportions) of the values in each category.
Make a frequency table and a relative frequency table of the following averages for previous AP
Stats students.
A C BF A BC D DF B CC C BB D AB D C
ABCDF
ABCDF
36642
.1428
.2857
.2857
.1905
.0952
Why make a picture?• It may reveal things you can’t see in
the table• It shows important features• It helps you tell about the data to
others
Things to Remember…• Context• Appropriate Scale• Area Principle• Label!oInclude units where applicable
Make a bar chart of the previous AP Stats averages by letter grade.
You may also see it like this…
A
B
C
D
F
0 1 2 3 4 5 6 7
What do we see in the graph?
Make a relative frequency bar chart of the previous AP Stats averages.
Pie Charts
Doesn’t add up to 100%50% does not look like halfPercentages of what whole?
Respondents could be in more than one category
Make a pie chart of the previous AP Stats averages.
ABCDF
ABCDF
.1428
.2857
.2857
.1905
.0952
How can we be sure it’s divided proportionally?
What do we see in the graph?
• A should look bigger than F• B and C should look the same• B and C should look twice the size of A• D should appear larger than A
• Can approximate areas• Can also use Geometry to calculate Central Angle
measures (cross-curricular)
Important Disclaimer:CAN ONLY USE BAR
CHARTS AND PIE CHARTS AS LONGS AS INDIVIDUALS
BEING STUDIED DO NOT FALL INTO MORE
THAN ONE CATEGORY.
The table below gives the distribution by
region of the population in the United
States in 1996.
58.5West93.1South62.1Midwest51.6NortheastPopulation(in millions)Region
Make a pie chart of the population data.
NE
MW
S
W
Homeworkp. 36-44 # 5, 7, 8, 10, 11, 13, 14
(due Monday)
Reminder:Due tomorrow-
1) p.16 Homework from Textbook 2) Reading Questions Ch.2-3