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 need to fill out the two-way frequency table and answer the questions.

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Step 1: Fill in what we know

We'll create a table with:
- Rows: Dogs, Cats, Total
- Columns: Freshmen, Sophomores, Total

Start filling in known values:

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

Now, let’s deduce the missing values.

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

So, Freshmen with dogs = 11

#### For Sophomores:
- Total sophomores = 20
- 13 have dogs → So, number who have cats = 20 - 13 = 7

So, Sophomores with cats = 7

Now fill in the rest.

#### Now compute totals:

- Dogs total = Freshmen dogs + Sophomore dogs = 11 + 13 = 24
- Cats total = Freshmen cats + Sophomore cats = 9 + 7 = 16
- Total students = 20 + 20 = 40

Final table:

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

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Answer the Questions:

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1. How many 10th graders have cats?

- 10th graders = sophomores
- From table: 7 sophomores 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

$$
\frac{16}{40} \times 100 = 40\%
$$

✔ Answer: 40%

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5. What percentage of the students surveyed were in 9th grade?

- Freshmen = 20
- Total = 40

$$
\frac{20}{40} \times 100 = 50\%
$$

✔ Answer: 50%

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6. What is the relative frequency of 9th grade dog owners?

- Relative frequency = (Number of 9th grade dog owners) / (Total number of students)
- 9th grade dog owners = 11
- Total students = 40

$$
\frac{11}{40} = 0.275 = 27.5\%
$$

✔ 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

$$
\frac{7}{20} = 0.35 = 35\%
$$

✔ Answer: 0.35 or 35%

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8. Is there an association between grade levels and pet choices?

Let’s compare:
- Freshmen:
- Dogs: 11/20 = 55%
- Cats: 9/20 = 45%
- Sophomores:
- Dogs: 13/20 = 65%
- Cats: 7/20 = 35%

→ More sophomores own dogs, fewer own cats compared to freshmen.

There is a slight trend: higher dog ownership in 10th grade, lower cat ownership.

But since both groups are small, and the difference isn't huge, we might say there is some evidence of an association, but not strong.

However, statistically, if we were testing for independence, we’d do a chi-square test. But here, based on observation:

✔ Answer: Yes, there appears to be a slight 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

✔ Answer: Dogs are more popular.

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10. Is this statement always true: A 10th grader is more likely to own a dog.

- 10th graders: 13 out of 20 own dogs → 65%
- 9th graders: 11 out of 20 own dogs → 55%

So yes, in this sample, 10th graders are more likely to own a dog.

But the word "always" makes it tricky.

The statement says "A 10th grader is more likely to own a dog" — this is true for this sample, but we can't say it's always true in general unless we have population data.

But in context of this survey, it is true.

Since the question asks whether it's always true, and we only have one sample, we must say:

✔ Answer: No, this statement is not always true — it is true in this case, but “always” implies it's universally true, which we cannot conclude from one sample.

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✔ 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, because "always" implies universal truth, but this conclusion is based only on this sample.

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Let me know if you'd like a visual version of the table or further explanation!