Glossary Terms:

Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core

Mathematics by HMH (2012) All Rights Reserved.

(Alg 1 Power Point Slides edited by

Mr. G. Weidinger, EWHS Goldsboro, NC)

Glossary Terms:

Joint relative frequency: is found by dividing a frequency that is not in the Total row or the Total column by the grand total.

Two-way Frequency table: a table listing two categorical variables who values have been paired.

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.





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.


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






Creating a Two-Way Relative Frequency Table:Jenna also recorded the gender of each student surveyed, complete the two-way frequency table below.


Boys

Girls

Totals

10 40

= .255 40

= .125 9 40

= .22524 40

= .60

8 40

= .207 40

= .1751 40

= .02516 40

= .40

18 40

= .4512 40

= .3010 40

= .2540 40

= 1.00



Boys 10 5 9 24

Girls 8 7 1 16

Totals 18 12 10 40





Creating a Two-Way Relative Frequency Table:


Boys

Girls

Totals

10 40

= .255 40

= .125 9 40

= .22524 40

= .60

8 40

= .207 40

= .1751 40

= .02516 40

= .40

18 40

= .4512 40

= .3010 40

= .2540 40

= 1.00


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%






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%


Boys 25% 12.5% 22.5% 60%

Girls 20% 17.5% 2.5% 40%

Totals 45% 30% 25% 100%






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%



Boys 10 5 9 24

Girls 8 7 1 16

Totals 18 12 10 40








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%






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%



Boys 10 5 9 24

Girls 8 7 1 16

Totals 18 12 10 40








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%





Graph the Two-Way Relative Frequency Table:

0

5

10

15

20

25

Boys

Dogs

Cats

Other

0

5

10

15

20

Girls

Dogs

Cats

Other

Dogs

Cats

OtherDogs

Cats

Other

DogsCats

Other

Dogs

Cats

Other


Boys 25% 12.5% 22.5% 60%

Girls 20% 17.5% 2.5% 40%

Totals 45% 30% 25% 100%

What benefit can these graphs provide in analyzing the data?

Visual analysis; quicker/faster comparison of the data; scales; colors

Boys Girls






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%

0

5

10

15

20

25

Boys Girls

Dogs

Cats

Other

0 10 20 30

Girls

Boys

Dog

Cats

Others

BoysGirls

0

5

10

15

20

25

Dogs

Cats

Other

What benefit can these graphs provide in analyzing the data?Visual analysis, quicker/faster comparison of the data, scales, colors






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%,


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Glossary Terms: