Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
I. Vocabulary
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.
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
II. 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
II. 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
III. 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
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
Cat
Other
Total
25%
12.5% 22.5%
60%
Girls
20%
17.5%
2.5%
40%
Totals
45%
30%
25%
100%
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
IV. 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.
10
Number of boys who prefer dogs:
= .556 = 55.6%
Number of students who prefer dogs: 18
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
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
Cats
Visual analysis;
quicker/faster
comparison of the
data; scales; colors
Other
Girls
Dogs
Cats
Dogs
Cats
Other
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
V. 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
25
Cats
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
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3
On-Core: 9-5 Two Way Frequency Tables
VI. 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