JOINT, MARGINAL, AND CONDITIONAL FREQUENCIES
STANDARDS:
Common Core State Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Attend to precision.
MCC9-12.S.ID.5 Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data (including joint,
marginal, and conditional relative frequencies). Recognize possible associations and
trends in the data.
BY THE END OF THIS LESSON, YOU SHOULD BE ABLE TO:
1.
Interpret data from a two-way frequency table
2.
Identify and interpret joint, marginal, and conditional
relative frequencies
3.
Create a conditional distribution table
4.
Create a relative frequency chart
TERMS
• Two-way Frequency table: a table listing two categorical variables
who values have been paired
• Joint relative frequency: is found by dividing a frequency that is
not in the Total row or the Total column by the grand total.
• Marginal relative frequency: is found by dividing a row total or a
column total by the grand total.
• Two-Way relative frequency table: displays both the joint relative
and marginal relative frequencies.
• Conditional relative frequency: is found by dividing a frequency
that is not in the Total row or Total column by the frequency’s row
total or column total.
TWO-WAY FREQUENCY TABLE
Watch this:
http://www.youtube.com/watch?v=aUwpxoaCV-w
CONDITIONAL DISTRIBUTIONS
Watch:
http://www.youtube.com/watch?v=-vLW7Ss7M94
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Creating a Relative Frequency Table:
Jenna asked 40 randomly selected students whether they
preferred dogs, cats or other pets.
Complete the table for both decimals and percents
Preferred Pet
Frequency
Relative Frequency
Decimals
Relative Frequency
Percents
Dog
Cat
Other
Total
18
12
10
40
18
= .45
40
12
= .30
40
10
= .25
40
40
= 1.00
40
45%
30%
25%
100%
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Creating a Two-Way Frequency Table:
Jenna also recorded the gender of each student.
The results are shown in the two-way frequency table. Find the
totals and answer the questions.
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7
1
16
Totals
18
12
10
40
40
1) How many total students took the survey?
2) How many total boys took the survey?
24
3) How many students said they like dogs as pets?
4) How many boys said they like dogs as pets?
18
10
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Creating a Two-Way Relative Frequency Table:
Jenna also recorded the gender of each student surveyed,
complete the two-way frequency table below.
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7
1
16
Totals
18
12
10
40
Preferred Pet
Dog
Cat
Boys
Girls
Totals
10
= .25
40
8
40 = .20
18
= .45
40
Other
Total
5
= .125 9 = .225 24 = .60
40
40
40
1
7
16
40 = .175 40 = .025 40 = .40
12
40
10
= 1.00
= .25
=
.30
40
40
40
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Creating a Two-Way Relative Frequency Table:
Preferred Pet
Boys
Girls
Totals
Dog
10
= .25
40
8
40 = .20
18
= .45
40
Cat
Other
Total
5
= .125 9 = .225 24 = .60
40
40
40
1
7
16
40 = .175 40 = .025 40 = .40
12
40
10
= 1.00
=
.25
40 = .30
40
40
State the percents for the table above.
Preferred Pet
Boys
Girls
Totals
Dog
Cat
Other
Total
25%
20%
45%
12.5%
17.5%
22.5%
2.5%
30%
25%
60%
40%
100%
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Creating a Two-Way Relative Frequency Table:
Preferred Pet
Dog
Boys
Girls
Totals
Cat
Other
Total
25%
12.5% 22.5%
60%
20%
45%
17.5%
30%
40%
100%
2.5%
25%
1) Find the joint relative frequency of students surveyed who are
girls and prefer dogs as pets.
20%
2) Find the joint relative frequency of students surveyed who are
boys and prefer cats as pets.
12.5%
3) Find the marginal RF of students surveyed who
prefer dogs as pets and then prefer cats as pets.
dogs - 45%
cats - 30%
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Calculating a Conditional Relative Frequency:
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7
1
16
Totals
18
12
10
40
Find the conditional relative frequency that a student surveyed
prefers cats as pets, given the student is a girl.
Number of girls who prefer cats:
Number of girls:
7
16
= .4375 = 43.75%
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Calculating a Conditional Relative Frequency:
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7
1
16
Totals
18
12
10
40
Find the conditional relative frequency that a student surveyed is a
girl, given that the student prefers cats as pets.
Number of girls who prefer cats:
Number of students who prefer cats:
7
= .583 = 58.3%
12
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Calculating a Conditional Relative Frequency:
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7
1
16
Totals
18
12
10
40
Find the conditional relative frequency that a student surveyed
prefers cats as pets, given the student is a boy.
Number of boys who prefer cats:
Number of boys:
5
24
= .208
= 20.8%
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Calculating a Conditional Relative Frequency:
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7
1
16
Totals
18
12
10
40
Find the conditional relative frequency that a student surveyed is
a boy, given that the student prefers dogs as pets.
Number of boys who prefer dogs:
Number of students who prefer dogs:
10
= .556 = 55.6%
18
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Finding Possible Associations and Trends
Jenna survey results (numbers vs percents).
Dog
Cat
Other
Total
Boys
10/25%
5/12.5%
9/22.5%
24/60%
Girls
8/20%
7/17.5%
1/2.5%
16/40%
Totals
18/45%
12/30%
10/25%
40/100%
1) Does the table reflect gender bias towards pets?
But, it does imply, boys like “other” pets more than girls: 22.5% to 2.5%,
2) If so, which gender, likes which pets the best?
NO
N/A
3) What are some examples of “other” pets?
Hamsters, gerbils, mice, rats,
snakes, rabbits, pigs, etc.,
4) Girls tend not to like which types of pets?
“other” types
RELATIVE FREQUENCY
Go here:
http://www.mathsisfun.com/data/relative-frequency.html
Make sure you try the 10 practice problems.
REVIEW:
Key concepts covered in this presentation:
1.
How to read a two-way frequency table
2.
Marginal and joint distributions
3.
Conditional distribution tables
4.
Relative frequency