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

Let's solve this step by step.

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Given Information:

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

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

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Step 1: Fill in the Two-Way Frequency Table

We'll use the data to complete the table:

| | Freshmen | Sophomores | Total |
|----------------|----------|------------|-------|
| Dogs | ? | 13 | ? |
| Cats | 9 | ? | ? |
| Total | 20 | 20 | 40 |

Now let’s find the missing values.

#### Freshmen:
- Total freshmen = 20
- 9 have cats → So, number of freshmen with dogs = 20 - 9 = 11

#### Sophomores:
- 13 have dogs → So, number of sophomores with cats = 20 - 13 = 7

#### Totals:
- Dogs total = 11 (freshmen) + 13 (sophomores) = 24
- Cats total = 9 (freshmen) + 7 (sophomores) = 16
- Grand total = 40

Now fill in the completed table:

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

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Now Answer the Questions:

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1. How many 10th graders have cats?
→ 10th graders = sophomores → 7 have cats.
✔ Answer: 7

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

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

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

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

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

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7. Out of the sophomores, what is the relative frequency of owning a cat?
→ Sophomores with cats = 7
→ Total sophomores = 20
→ Relative frequency = 7 / 20 = 0.35 or 35%
✔ Answer: 0.35 (or 35%)

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

But let’s look at proportions:
- Freshmen: 9/20 = 45% cats, 55% dogs
- Sophomores: 7/20 = 35% cats, 65% dogs

So sophomores are more likely to own dogs, and freshmen are more likely to own cats.

This suggests a slight difference in pet preference by grade, so yes, there may be an association.

✔ Answer: Yes, there is an association. Sophomores are more likely to own dogs than freshmen.

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

✔ Answer: Dogs

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10. Is this statement always true: A 10th grader is more likely to own a dog?
→ For 10th graders (sophomores): 13 dogs, 7 cats → 13/20 = 65% have dogs
→ So yes, they are more likely to own a dog.

But the question says "always true" — we only have data from one survey. We can’t say it’s *always* true in general, just that in this sample, it is true.

But based on the given data, the statement is true for this group.

However, “always” implies universal truth, which we cannot confirm from one sample.

✔ Answer: No, the statement is not always true in general, but it is true for this sample.
(Or: "No, because 'always' implies it's universally true, but we only have data from one survey.")

But if interpreting within the context of the data:

✔ Answer: Yes, based on this data, a 10th grader is more likely to own a dog (65% vs 35%).

But since it says "always", the best answer is:

> ✘ No, because the statement uses "always," which implies it's universally true. This conclusion is only valid for this specific survey.

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✔ Final Answers:

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 an association; sophomores are more likely to own dogs.
9. Dogs
10. No, the statement is not always true; it's true for this sample, but "always" makes it too strong.

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Let me know if you'd like a version formatted as a printable worksheet!