Two-Way
Frequency Tables
SUMMARIZE CATEGORICAL DATA
Focus 6 Learning Goal – (HS.S-ID.A.1, HS.S-ID.A.2, HS.S-ID.A.3, HS.S-ID.B.5) =
Students will summarize, represent and interpret data on a single
count or measurement variable.
4
In addition to level
3.0 and above and
beyond what was
taught in class, the
student may:
· Make connection
with other concepts
in math
· Make connection
with other content
areas.
3
The student will summarize,
represent, and interpret data
on a single count or
measurement variable.
- Comparing data includes
analyzing center of data
(mean/median), interquartile
range, shape distribution of a
graph, standard deviation
and the effect of outliers on
the data set.
- Read, interpret and write
summaries of two-way
frequency tables which
includes calculating joint,
marginal and relative
frequencies.
2
1
The student will be
able to:
- Make dot plots,
histograms, box
plots and two-way
frequency tables.
- Calculate
standard deviation.
- Identify normal
distribution of data
(bell curve) and
convey what it
means.
With help from
the
teacher, the
student has
partial success
with summarizing
and interpreting
data displayed in
a dot plot,
histogram, box
plot or frequency
table.
0
Even with
help, the
student has
no success
understandin
g statistical
data.
Numerical vs. Categorical Data

Numerical data includes data that are numbers:
height, weight, age, price, temperature, test
scores, etc.

Categorical data that isn’t numeric would be
like: eye color, hair color, favorite ice cream,
favorite superhero, city of birth, etc.

Two-Way Table a table listing two categorical
variables whose values have been paired.
Data was collected from men and women about
their favorite DC comic book superheroes: Wonder
Woman, Batman, or Superman.

100 men and 100 women were surveyed.

The data is displayed in a two-way frequency table.

Talk with the person next to you to determine how to read
the table. What do the labels mean?
Data was collected from men and women about
their favorite DC comic book superheroes: Wonder
Woman, Batman, or Superman.

We learn some basic information from the table
when it is displayed in this format.

87 people prefer Wonder Woman.

Of the 87 people who prefer Wonder Woman,
62 of them were women.
Types of Frequencies:


Joint Frequency: The data in the middle cells.
(The yellow section.)

These are the ratios of the frequency in a particular category and the grand total
number of data values.

It is called joint frequency because you are joining one variable from the row and
one variable from the column.
Marginal Frequency: The data on the far right and the bottom.
(The blue
section.)


These are the ratios of the sum of the joint relative frequency in a row or column
and the grand total number of data values.
Conditional relative frequency: The ratio of a joint relative frequency
and related marginal relative frequency.

This is what you did in Linear Algebra.
Conditional Frequency:
(A refresher from last year .)

To calculate Conditional Frequency, you
divide the cell total by the row total.

Calculate the conditional frequency of males
who like Wonder Woman.


Calculate the conditional frequency of
females who like Wonder Woman.


62/100 = 62%.
Calculate the conditional frequency of males
who like Batman.


25/100 = 25%.
40/100 = 40%
Fill in the rest of the middle section of the table.
25%
40%
35%
62%
23%
15%
Conditional Frequency:
(A refresher from last year .)

To fill in the row total for Male, divide Male
Total by the grand Total. (100/200)

To fill in the row total for Female, divide
Female Total by the grand Total. (100/200)

To fill in the column total for WW, divide WW
Total by the grand Total. (87/200)

To fill in the column total for BW, divide BM
Total by the grand Total. (63/200)

To fill in the column total for SM, divide SM
Total by the grand Total. (50/200)

To fill in the column total for TOTAL, add up
the percents in that column or in that row.
25%
40%
35%
50%
62%
23%
15%
50%
43.5% 31.5% 25%
100%
Conditional Frequency:


These are the types of questions that can
be answered from conditional frequency
tables.

What percent of males prefer Batman?

What percent of females prefer Superman?

What percent of the males surveyed prefer
Wonder Woman?
A question you cannot answer from this
table is, “What percent of the total people
surveyed were women who liked Wonder
Woman?”

The answer of 62% is not correct. That is the
percent of JUST the women who like Wonder
Woman.
Joint “Relative” Frequency:

Relative or Joint Relative Frequency will allow you
to answer the question, “What percent of the
people surveyed were women who like Wonder
Woman?”

Calculate Relative Frequency by dividing the cell
total by the grand total.

Divide male votes for Wonder Woman by the
grand total.


Divide female votes for Wonder Woman by the
grand total.


25/200 = 0.125 or 12.5%
62/200 = 0.310 or 31%
Finish filling in the table.
12.5% 20% 17.5%
31%
11.5% 7.5%
Calculate Relative Frequencies:
12.5% 20% 17.5% 50%
31%
11.5% 7.5% 50%
43.5% 31.5% 25% 100%

To fill in the row total, add up all of the percents in that row.

To fill in the column total, add up all of the percents in that column.

Now that the table has been changed to percents, you can make
predictions.

What is the probability that a person picked at random from this
group will be a female that likes Wonder Woman? 31%

What is the probability that a person picked at random from this
group will be a male who likes Superman? 17.5%
Marginal Frequencies

These are the ratios of the sum of the joint
relative frequency in a row or column and
the grand total number of data values.

These frequencies were calculated when
you made the Relative Frequency table.

The marginal frequencies answer these
types of questions:

What percent of the people surveyed were
female?

What percent of the people surveyed liked
Superman?

What percent of the people surveyed like
Batman?
12.5% 20% 17.5% 50%
31%
11.5% 7.5% 50%
43.5% 31.5% 25% 100%