Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
(Alg 1 Power Point Slides edited by
Mr. G. Weidinger, EWHS Goldsboro, NC)
NC Common Core Standards
• 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.
Objectives
• Create: relative frequency, two-way frequency, and two-way relative
frequency tables, in addition to recognizing associations and trends
• Calculate and interpret a conditional relative frequency data, to include
joint and marginal
• Using the appropriate graph, to graph the data and analyze the results
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
(Alg 1 Power Point Slides edited by
Mr. G. Weidinger, EWHS Goldsboro, NC)
Glossary 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.
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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
Dog
Cat
Other
Total
18
12
10
40
Relative Frequency
Decimals
18
= .45
40
12
= .30
40
10
= .25
40
40
= 1.00
40
Relative Frequency
Percents
45%
30%
25%
100%
Frequency
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Warm-up 1/17/2013
Mr. G. Weidinger, EWHS Goldsboro, NC)
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
1) How many total students took the survey? 40
2) How many total boys took the survey? 24
3) How many students said they like dogs as pets? 18
4) How many boys said they like dogs as pets? 10
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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
Preferred Pet
Dog
Cat
Boys
Girls
Totals
10
= .25
40
8
40 = .20
18
= .45
40
Other
40
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
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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%
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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%
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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%
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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%
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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.
10
Number of boys who prefer dogs:
= .556 = 55.6%
Number of students who prefer dogs: 18
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
Graph the Two-Way Relative Frequency Table:
Preferred Pet
Dog
Cat
Other
Total
Boys
25%
12.5%
22.5%
60%
Girls
20%
17.5%
2.5%
40%
Totals
45%
30%
25%
100%
Girls
Boys
20
25
20
15
Dogs
10
Cats
Other
5
What benefit can 15
10
these graphs
provide in
5
analyzing the data?
Dogs
Cats
Other
0
0
Boys
Other
Dogs
Dogs
Cats
Other
Visual analysis;
quicker/faster
comparison of the
data; scales; colors
Other
Girls
Dogs
Cats
Dogs
Cats
Other
Cats
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
Graph the Two-Way Relative Frequency Table:
Preferred Pet
Dog
Cat
Other
Total
Boys
25%
12.5%
22.5%
60%
Girls
20%
17.5%
2.5%
40%
Totals
45%
30%
25%
100%
25
20
Boys
15
Dogs
10
Cats
Other
5
Dog
Cats
25
Others
20
Girls
15
0
Boys
Girls
Dogs
10
Cats
Other
5
0
10
20
30
0
Boys
Girls
What benefit can these graphs provide in analyzing the data?
Visual analysis, quicker/faster comparison of the data, scales, colors
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All
(Alg 1 Power Point Slides edited by
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
Mr. G. Weidinger, EWHS Goldsboro, NC)
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? NO
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? 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
Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All