Two-way tables: joint, marginal and conditional relative frequencies

Answer Key - Grade 9 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. Read this first

   Relative frequency table: each cell is a percent of all 200 students

   	Pizza	Salad	Soup	Total
   Early lunch	5%	26%	27%	58%
   Late lunch	17%	15%	10%	42%
   Total	22%	41%	37%	100%

2. 1.

   Each cell of Ari's table is a percent of all 200 students. Of the students in the "Early lunch" row, what percent choose salad, to the nearest whole percent?

   45

3. Relative frequency table: each cell is a percent of all 50 seedlings

   	Flowered	No flowers	Total
   Sunny window	20%	8%	28%
   Shady shelf	28%	44%	72%
   Total	48%	52%	100%

4. 2.

   Each cell of Bo's table is a percent of all 50 seedlings. Of the seedlings in the "Shady shelf" row, what percent flowered, to the nearest whole percent?

   39

5. Relative frequency table: each cell is a percent of all 100 club members

   	Zoo	Museum	Aquarium	Total
   Science club	13%	30%	26%	69%
   Art club	9%	17%	5%	31%
   Total	22%	47%	31%	100%

6. 3.

   Each cell of Esme's table is a percent of all 100 club members. Of the club members in the "Art club" row, what percent vote for the zoo, to the nearest whole percent?

   29

7. Relative frequency table: each cell is a percent of all 200 students

   	Passed the quiz	Did not pass	Total
   Went to review	26%	15%	41%
   Skipped review	30%	29%	59%
   Total	56%	44%	100%

8. 4.

   Each cell of Jun's table is a percent of all 200 students. Of the students in the "Went to review" row, what percent passed the quiz, to the nearest whole percent?

   63

9. Two-way table of singers and players, with no totals yet

   	Summer	Fall	Winter
   Band	20	25	29
   Choir	30	21	30

10. 5.

    Kira's table has no totals yet. Of the singers and players in the "Summer" column, what percent are in band, to the nearest whole percent?

    40

11. Two-way table of students, with no totals yet

    	Walks	Bikes	Bus
    9th grade	10	7	26
    10th grade	30	18	28

12. 6.

    Noah's table has no totals yet. Of the students in the "10th grade" row, what percent bike to school, to the nearest whole percent?

    24

13. Relative frequency table: each cell is a percent of all 100 students

    	Entered the fair	Did not enter	Total
    Art class	25%	7%	32%
    No art class	25%	43%	68%
    Total	50%	50%	100%

14. 7.

    Each cell of Pia's table is a percent of all 100 students. Is there a link between taking art class and whether students enter the art fair?

    • Yes: being in art class makes students enter the art fair.
    • No: the "Entered the fair" cells are equal, 25% of all students in each row.
    • Yes: other students tend to enter the art fair more often than art-class students.
    • Yes: art-class students tend to enter the art fair more often than other students.

15. Relative frequency table: each cell is a percent of all 200 campers

    	Flew a kite	Went swimming	Total
    Cabin A	12%	15%	27%
    Cabin B	12%	61%	73%
    Total	24%	76%	100%

16. 8.

    Each cell of Ren's table is a percent of all 200 campers. Is there a link between the cabin and whether campers fly a kite?

    • Yes: Cabin B campers tend to fly a kite more often than Cabin A campers.
    • Yes: being in Cabin A makes campers fly a kite.
    • No: the "Flew a kite" cells are equal, 12% of all campers in each row.
    • Yes: Cabin A campers tend to fly a kite more often than Cabin B campers.

17. Relative frequency table: each cell is a percent of all 100 volunteers

    	Planted a tree	Picked up litter	Total
    Morning shift	27%	8%	35%
    Afternoon shift	49%	16%	65%
    Total	76%	24%	100%

18. 9.

    Each cell of Tala's table is a percent of all 100 volunteers. Is there a link between the shift and whether volunteers plant a tree?

    • Yes: being on the morning shift makes volunteers plant a tree.
    • No: about the same share of each group tends to plant a tree.
    • Yes: morning volunteers tend to plant a tree more often than afternoon volunteers.
    • Yes: the "Afternoon shift" row has far more of all volunteers who planted a tree, 49% against 27%.

19. Relative frequency table: each cell is a percent of all 200 students

    	Reusable bottle	No bottle	Total
    9th grade	19%	17%	36%
    10th grade	35%	29%	64%
    Total	54%	46%	100%

20. 10.

    Each cell of Zee's table is a percent of all 200 students. Is there a link between the grade and whether students bring a reusable bottle?

    • Yes: the "10th grade" row has far more of all students who bring a reusable bottle, 35% against 19%.
    • Yes: 10th graders tend to bring a reusable bottle more often than 9th graders.
    • No: about the same share of each group tends to bring a reusable bottle.
    • Yes: being in 10th grade makes students bring a reusable bottle.