Two-Way Frequency Tables Notes and Worksheets - Lindsay Bowden - Free Printable

Let’s solve this step by step.

We are told:
- 20 freshmen and 20 sophomores were surveyed → total students = 40
- 13 sophomores said they had dogs → so sophomores with cats = 20 - 13 = 7
- Out of the 20 freshmen, 9 had cats → so freshmen with dogs = 20 - 9 = 11

Now let’s fill in the table:

| | Freshmen | Sophomores | Total |
|----------|----------|------------|-------|
| Dogs | 11 | 13 | 24 |
| Cats | 9 | 7 | 16 |
| Total | 20 | 20 | 40 |

Check:
Dogs total: 11 + 13 = 24 ✔️
Cats total: 9 + 7 = 16 ✔️
Freshmen total: 11 + 9 = 20 ✔️
Sophomores total: 13 + 7 = 20 ✔️
Grand total: 24 + 16 = 40 or 20 + 20 = 40 ✔️

Now answer each question:

1. How many 10th graders have cats?
→ 10th graders = sophomores → from table: 7

2. How many students own dogs?
→ Total dogs = 24

3. How many freshmen own dogs?
→ From table: 11

4. What percentage of students own cats?
→ Cats total = 16, total students = 40
→ (16 ÷ 40) × 100 = 40%

5. What percentage of the students surveyed were in 9th grade?
→ 9th graders = freshmen = 20
→ (20 ÷ 40) × 100 = 50%

6. What is the relative frequency of 9th grade dog owners?
→ Relative frequency = part / whole
→ 9th grade dog owners = 11, total students = 40
→ 11 ÷ 40 = 0.275 or 27.5%

7. Out of the sophomores, what is the relative frequency of owning a cat?
→ Sophomores with cats = 7, total sophomores = 20
→ 7 ÷ 20 = 0.35 or 35%

8. Is there an association between grade levels and pet choices?
→ Let’s compare percentages:
- Freshmen: 11/20 = 55% dogs, 45% cats
- Sophomores: 13/20 = 65% dogs, 35% cats
→ Since the percentages are different, yes — there is an association. Sophomores are more likely to have dogs than freshmen.

9. Which pet choice is more popular?
→ Dogs: 24 students, Cats: 16 students → Dogs are more popular.

10. Is this statement always true: A 10th grader is more likely to own a dog.
→ In this survey, 65% of sophomores (10th graders) own dogs vs 55% of freshmen. So based on this data, it’s true for this group. But “always” means every time, everywhere — we can’t say that from one survey. So the answer is no — it’s not *always* true, just true in this case.

Final Answer:
1. 7
2. 24
3. 11
4. 40%
5. 50%
6. 0.275 (or 27.5%)
7. 0.35 (or 35%)
8. Yes
9. Dogs
10. No