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

Let's solve this step by step.

We are given:

- 20 freshmen (9th grade)
- 20 sophomores (10th grade)
- 13 sophomores have dogs
- 9 freshmen have cats

We need to fill out a two-way frequency table based on this information.

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Step 1: Fill in the known values

We'll create a table with rows for Dogs, Cats, and Total, and columns for Freshmen, Sophomores, and Total.

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

Now, let’s deduce the missing values.

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Step 2: Use totals to find missing numbers

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

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

Now we can fill in the rest:

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

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Now, answer each question using the completed table.

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1. How many 10th graders have cats?

→ 10th graders = sophomores
→ Number who have cats = 7

✔ Answer: 7

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2. How many students own dogs?

→ Total dogs = 11 (freshmen) + 13 (sophomores) = 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 students = 40
→ Total cat owners = 16
→ Percentage = (16 / 40) × 100 = 40%

✔ Answer: 40%

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

→ 9th grade = freshmen = 20
→ Total students = 40
→ Percentage = (20 / 40) × 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)
= 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?

→ Number of sophomores who own 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 analyze:

- Freshmen:
- Dogs: 11/20 = 55%
- Cats: 9/20 = 45%

- Sophomores:
- Dogs: 13/20 = 65%
- Cats: 7/20 = 35%

So, sophomores are more likely to have dogs, while freshmen are more balanced, but slightly favor dogs.

But the difference is not huge. Let's look at relative frequencies within each group:

- Among freshmen: 55% have dogs, 45% have cats
- Among sophomores: 65% have dogs, 35% have cats

So dogs are more popular among sophomores, but both groups prefer dogs over cats.

Is this a strong association? Not really — the trend is similar, just slightly stronger for sophomores.

But since dog ownership increases from 9th to 10th grade, there might be a weak association.

However, no clear strong pattern — so we might say there is a weak association, or not enough evidence for a strong one.

But let's think carefully: The proportion of dog owners is higher in 10th grade than 9th.

So yes, grade level may be associated with pet choice.

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

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9. Which pet choice is more popular?

Compare total numbers:

- Dogs: 24
- Cats: 16

So 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?

Let’s check:

- Probability that a 10th grader owns a dog = 13 / 20 = 65%
- Probability that a 9th grader owns a dog = 11 / 20 = 55%

So yes, a 10th grader is more likely to own a dog in this sample.

But the question says "always true".

Is it always true? No — this is based on one survey. We don’t know if this holds in general.

So the statement is true in this case, but not necessarily always true.

✔ Answer: No, it is not always true. It is true in this data set, but not guaranteed to be true in all cases.

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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 a weak association; sophomores are more likely to own dogs.
9. Dogs
10. No, it is not always true. It is true in this data, but not guaranteed in all cases.

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