Notes ­ 2 way tables.notebook
February 21, 2014
Bivariate data consists of pairs of linked numerical
observations, or frequencies of things in categories.
Numerical bivariate data can be presented as a set
of ordered pairs, as a table of values, or as a graph
on the coordinate plane.
• An example would be the number of people in
certain after school activities at your school broken
down by gender.
Notes ­ 2 way tables.notebook
February 21, 2014
A bivariate or two­way frequency table is often used with
data from two categories. Two­way frequency charts
are made of cells. The number in each cell is the
frequency of things that fit both the row and column
categories for the cell.
Example: The table below displays the results of a survey
that examined the relationship between gender and
video game play.
Play Daily
Play TOTAL
Occasionally
Boys
16
8
24
Girls
4
12
16
TOTAL
20
20
40
Notes ­ 2 way tables.notebook
February 21, 2014
A Relative Frequency Table shows joint and marginal relative frequencies.
Joint Relative Frequencies are the values in each category divided by the total number of values.
Marginal Relative Frequencies are found by the total of a row or column divided by the total number of values. (They should also be the sum of the row or column)
Table from Survey
Play Daily
Relative Frequency Table Play TOTAL
Occasionally
Play Daily
Play TOTAL
Occasionally
Boys
16
8
24
Boys
16/40 = .40
.20
.60
Girls
4
12
16
Girls
.10
.30
.40
TOTAL
20
20
40
TOTAL
.50
.50
1
= Joint Relative Frequency
Round to the nearest hundredth!
= Marginal Relative Frequency
Notes ­ 2 way tables.notebook
February 21, 2014
Relative Frequency Tables can also be
shown in Percents
Play Daily
Play TOTAL
Occasionally
Boys
16
8
24
Girls
4
12
16
TOTAL
20
20
40
Play Daily
Play TOTAL
Occasionally
Boys
.40
.20
.60
Girls
.10
.30
.40
TOTAL
.50
.50
1
Play Daily
Play TOTAL
Occasionally
Boys
40%
20%
60%
Girls
10%
30%
40%
TOTAL
50%
50%
100%
Table from
Survey
Relative
Frequency Table
in Decimals
(Probability)
Relative
Frequency Table
in Percents
Notes ­ 2 way tables.notebook
February 21, 2014
Make a table of the joint and marginal frequencies.
Male
Female
TOTAL
Band
12
21
33
Chorus
15
17
32
Yearbook
28
7
35
TOTAL
55
45
100
Male
Female
TOTAL
Band
Chorus
Yearbook
TOTAL
Round to the nearest hundredth!
Notes ­ 2 way tables.notebook
February 21, 2014
Make a table of the joint and marginal frequencies
in Percents.
For
Against
TOTAL
Students
5
37
42
Parents
20
18
38
TOTAL
25
55
80
For
Against
TOTAL
Students
Parents
TOTAL
Round to the nearest hundredth!
Notes ­ 2 way tables.notebook
February 21, 2014
The frequency table below shows the results of a poll of
80 randomly selected high school students who were
asked if they prefer math or English. Make a table of
joint and marginal frequencies.
9th 10th 11th 12th TOTAL
Grade Grade Grade Grade
9th 10th 11th 12th TOTAL
Grade Grade Grade Grade
Math
10
12
11
8
41
Math
English
12
11
8
8
39
English
TOTAL
22
23
19
16
80
TOTAL
What is the probability a student polled was in the 9th
grade?
What type of frequency is this? (Joint or Marginal)
What is the probability a student polled is in the 9th
grade and prefers math?
What type of frequency is this? (Joint or Marginal)
Notes ­ 2 way tables.notebook
February 21, 2014
The frequency table below shows the results of a poll of
80 randomly selected high school students who were
asked if they prefer math or English.
9th 10th 11th 12th TOTAL
Grade Grade Grade Grade
9th 10th 11th 12th TOTAL
Grade Grade Grade Grade
Math
10
12
11
8
41
Math
.13
.15
.14
.10
.51
English
12
11
8
8
39
English
.15
.14
.10
.10
.49
TOTAL
22
23
19
16
80
TOTAL
.28
.29
.24
.20
80
What percent of the students polled like Math?
What type of frequency is this? (Joint or Marginal)
What percent of the students polled are in 12th grade
and like English?
What type of frequency is this? (Joint or Marginal)
Notes ­ 2 way tables.notebook
February 21, 2014
A Conditional Relative Frequency can be found by
dividing the joint relative frequency by the marginal
relative frequency.
9th 10th 11th 12th TOTAL
Grade Grade Grade Grade
9th 10th 11th 12th TOTAL
Grade Grade Grade Grade
Math
10
12
11
8
41
Math
.13
.15
.14
.10
.51
English
12
11
8
8
39
English
.15
.14
.10
.10
.49
TOTAL
22
23
19
16
80
TOTAL
.28
.29
.24
.20
80
Example: Given the student is in the 11th grade, what is
the probability they like math?
Example: Of the students that like English, what percent
are in the 10th grade?
Notes ­ 2 way tables.notebook
February 21, 2014
Probablity or Percent from a Relative Frequency Table:
Byron asked fellow high school students and their parents if
they support a proposal to replace the current school food
vendor with a new food vendor.
New Vendor
Current
Vendor
Total
Parents
0.36
0.14
0.50
Students
0.24
0.26
0.50
Total
0.60
0.40
1.00
What is the probability that a person polled supports a new
vendor?
What is the probability a person polled was a student?
Given the person was a student, what is the probability
they support the current vendor?
Given the person supported the new vendor, what is the
probability they were a parent?