two-way frequency tables

TWO-W

AY F

REQUENCY

TABLE

S

J O I N T , M A R G I N A L , A N D C O N D I T I O N A L F R E Q U E N C I E S

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

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 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

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 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

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 40

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 Tables

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 Cat Other Total

Boys 25% 12.5% 22.5% 60%

Girls 20% 17.5% 2.5% 40%

Totals 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

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 10 5 9 24

Girls 8 7 1 16

Totals 18 12 10 40

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 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 students who prefer cats:

Number of girls who prefer cats:

7 12

= .583

= 58.3%

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 10 5 9 24

Girls 8 7 1 16

Totals 18 12 10 40

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 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 students who prefer dogs:

Number of boys who prefer dogs:

10

18= .556

= 55.6%

Finding Possible Associations and TrendsJenna 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?

2) If so, which gender, likes which pets the best? 3) What are some examples of “other” pets?

NO

N/AHamsters, 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 Tables

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