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

Let's solve this step by step.

---

Given Information:

- 20 freshmen (9th grade) and 20 sophomores (10th grade) were surveyed.
- 13 sophomores have dogs.
- 9 freshmen have cats.

We are to create a two-way frequency table and answer the questions.

---

Step 1: Fill in the Two-Way Frequency Table

We'll build the table using the given data.

#### Knowns:
- Total freshmen = 20
- Total sophomores = 20
- Total students = 40
- Freshmen with cats = 9 → So, freshmen with dogs = 20 - 9 = 11
- Sophomores with dogs = 13 → So, sophomores with cats = 20 - 13 = 7

Now fill in the table:

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

> ✔ We now have a complete two-way frequency table.

---

Now Answer the Questions:

---

1. How many 10th graders have cats?
→ Sophomores (10th graders) with cats = 7

✔ Answer: 7

---

2. How many students own dogs?
→ Total dogs = 11 (freshmen) + 13 (sophomores) = 24

✔ Answer: 24

---

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

✔ Answer: 11

---

4. What percentage of students own cats?
→ Total cat owners = 16
→ Total students = 40
→ Percentage = (16 / 40) × 100 = 40%

✔ Answer: 40%

---

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

✔ Answer: 50%

---

6. What is the relative frequency of 9th grade dog owners?
→ Relative frequency = (Number of 9th-grade dog owners) / (Total number of students)
= 11 / 40 = 0.275 or 27.5%

✔ Answer: 0.275 or 27.5%

---

7. Out of the sophomores, what is the relative frequency of owning a cat?
→ Number of sophomores with cats = 7
→ Total sophomores = 20
→ Relative frequency = 7 / 20 = 0.35 or 35%

✔ Answer: 0.35 or 35%

---

8. Is there an association between grade levels and pet choices?
Let’s compare:
- Freshmen: 9 cats, 11 dogs → More dogs
- Sophomores: 7 cats, 13 dogs → More dogs

Both grades prefer dogs over cats. But let’s check proportions:
- Freshmen: 9/20 = 45% cats
- Sophomores: 7/20 = 35% cats

So freshmen are more likely to have cats, sophomores are more likely to have dogs.

This suggests a slight association: grade level may influence pet preference.

✔ Answer: Yes, there appears to be a weak association — sophomores are more likely to own dogs than freshmen.

---

9. Which pet choice is more popular?
→ Dogs: 24 out of 40 = 60%
→ Cats: 16 out of 40 = 40%

✔ Answer: Dogs are more popular.

---

10. Is this statement always true: A 10th grader is more likely to own a dog?
Let’s calculate:
- Probability a 10th grader owns a dog = 13/20 = 65%
- Probability a 9th grader owns a dog = 11/20 = 55%

So yes, 10th graders are more likely to own a dog than 9th graders.

But the question asks: "Is this statement always true?"

The word "always" makes it tricky. The statement says: *"A 10th grader is more likely to own a dog."*

In this survey, yes, but we can't say it's always true for all populations — this is just one sample.

However, based on this data, it is true that 10th graders are more likely to own a dog.

But since the question says "always true", and we don’t have data beyond this sample, we must say:

✘ No, it is not always true — this is only true in this survey. It might not hold in other schools or populations.

✔ Answer: No, the statement is not always true; it is only true based on this sample.

---

✔ Final Answers Summary:

1. 7
2. 24
3. 11
4. 40%
5. 50%
6. 0.275 or 27.5%
7. 0.35 or 35%
8. Yes, there is a slight association — sophomores are more likely to own dogs.
9. Dogs
10. No, the statement is not always true — it's only true in this sample.

Let me know if you'd like a version with the filled table!