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 ID: 447650
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Slide1
Two-Way Frequency Tables
Joint, Marginal, and Conditional FrequenciesSlide2
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. Slide3
By the end of this lesson, you should be able to:
Interpret data from a two-way frequency table
Identify and interpret joint, marginal, and conditional relative frequencies
Create a conditional distribution table
Create a relative frequency chartSlide4
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. Slide5
Two-Way Frequency Table
Watch this:
http://www.youtube.com/watch?v=aUwpxoaCV-w
Slide6
Conditional Distributions
Watch:
http://www.youtube.com/watch?v=-vLW7Ss7M94
Slide7
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
Frequency
18
12
10
40
Relative Frequency Decimals
Relative Frequency Percents
18 40
= .45
45%
12 40
= .30
30%
10 40
= .25
25%
40 40
= 1.00
100%
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency TablesSlide8
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
24Girls87116Totals
18
12
10
40
1) How many total students took the survey?
2) How many total boys took the survey?
3) How
many students said they like dogs as pets?
4) How many boys said they like dogs as pets?
40
24
18
10
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency TablesSlide9
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
Girls
Totals
10
40
= .25
5
40
= .125
9
40
= .225
24
40
= .60
8
40
= .20
7
40
= .175
1
40
= .025
16
40
= .40
18
40
= .45
12
40
= .30
10
40
= .25
40
40
= 1.00
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7
1
16
Totals
18
12
10
40Slide10
Creating a Two-Way Relative Frequency Table:
Preferred Pet
Dog
Cat
Other
Total
Boys
Girls
Totals
10
40
= .25
5
40
= .125
9
40
= .225
24
40
= .60
8
40
= .20
7
40
= .175
1
40
= .025
16
40
= .40
18
40
= .45
12
40
= .30
10
40
= .25
40
40
= 1.00
Preferred Pet
Dog
Cat
Other
Total
Boys
Girls
Totals
State the percents for the table above.
25%
12.5%
22.5%
60%
20%
17.5%
2.5%
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 TablesSlide11
Creating a Two-Way Relative Frequency Table:
1) Find the joint relative frequency of students surveyed who are girls and prefer dogs as pets.
3
) Find the marginal RF of students surveyed
who prefer
dogs as pets and then prefer cats as pets.
dogs - 45%
12.5%
2) Find the joint relative frequency of students surveyed who are boys and prefer cats as pets.
20%
cats - 30%
Preferred Pet
Dog
CatOtherTotalBoys 25%12.5%22.5%60%Girls20%17.5%2.5%40%Totals45%30%
25%
100%
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency TablesSlide12
Calculating a Conditional Relative Frequency:
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
Preferred Pet
Dog
Cat
Other
Total
Boys 105924Girls87116Totals
18
12
10
40Slide13
Calculating a Conditional Relative Frequency:
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7116Totals
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 students who prefer cats:
Number of girls who prefer cats:
7
12
= .583
= 58.3%Slide14
Calculating a Conditional Relative Frequency:
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
Preferred Pet
Dog
Cat
Other
Total
Boys 105924Girls87116Totals
18
12
10
40Slide15
Calculating a Conditional Relative Frequency:
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables
Preferred Pet
Dog
Cat
Other
Total
Boys
10
5
9
24
Girls
8
7116Totals
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 students who prefer dogs:
Number of boys who prefer dogs:
10
18
= .556
= 55.6%Slide16
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%Totals18/45%12/30%10/25%40/100%
1) Does the table reflect gender bias towards pets?
2) If so, which gender, likes which pets the best?
3) What are some examples of “other” pets?
NO
N/A
Hamsters, gerbils, mice, rats, snakes, rabbits, pigs, etc.,
4) Girls tend not to like which types of pets?
“other” types
But, it does imply, boys like “other” pets more than girls: 22.5% to 2.5%,
Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency TablesSlide17
Relative Frequency
Go here:
http://www.mathsisfun.com/data/relative-frequency.html
Make sure you try the 10 practice problems.Slide18
Review:
Key concepts covered in this presentation:
How to read a two-way frequency table
Marginal and joint distributions
Conditional distribution tables
Relative frequency