Solved Use the two way frequency tables below to answer the ... - Free Printable

Let me work through each question step by step.

First Table: Pets Survey

The table shows:
- Male with Pets: 24, No Pets: 11
- Female with Pets: 27, No Pets: 10

First, I need to find the totals:
- A (Male Total) = 24 + 11 = 35
- B (Female Total) = 27 + 10 = 37
- C (Pets Total) = 24 + 27 = 51
- D (No Pets Total) = 11 + 10 = 21
- E (Grand Total) = 35 + 37 = 72 (or 51 + 21 = 72) ✓

F. What is the relative frequency of males that have a pet?

Relative frequency means: (number we want) / (total in that group)

For males that have a pet:
- Males with pets = 24
- Total males = 35
- Relative frequency = 24/35

Let me calculate this: 24 ÷ 35 = 0.6857... ≈ 0.686 or as a fraction 24/35

G. What is the relative frequency of females that do not have a pet?

For females without pets:
- Females without pets = 10
- Total females = 37
- Relative frequency = 10/37

Let me calculate: 10 ÷ 37 = 0.2703... ≈ 0.270 or as a fraction 10/37

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Second Table: Food Preferences

The table shows:
- Teachers: Italian=14, Mexican=18, American=11, Total=43
- Students: Italian=42, Mexican=24, American=57, Total=123
- Grand Total: 166

H. What percentage of the students preferred Italian food?

- Students who prefer Italian = 42
- Total students = 123
- Percentage = (42/123) × 100

Let me calculate: 42 ÷ 123 = 0.3415...
0.3415 × 100 = 34.15% ≈ 34.1% or 34%

I. What percentage of the teachers preferred Mexican food?

- Teachers who prefer Mexican = 18
- Total teachers = 43
- Percentage = (18/43) × 100

Let me calculate: 18 43 = 0.4186...
0.4186 × 100 = 41.86% ≈ 41.9% or 42%

J. How many total people were in both surveys?

This asks for the grand total from both tables combined:
- First survey (pets): 72 people
- Second survey (food): 166 people
- Total = 72 + 166 = 238

Wait, let me re-read this question. It says "both surveys" - this could mean:
1. The total number of people across both surveys (72 + 166 = 238), OR
2. Just asking about the second survey which has a total of 166

Looking at the context, it seems like it's asking for the grand total shown in the second table, which is 166. But "both surveys" suggests adding them together.

Actually, looking more carefully at the wording "How many total people were in both surveys?" - this most likely means the sum of all participants from both surveys: 72 + 166 = 238.

Let me verify my calculations one more time:

F: 24/35 = 0.6857...
G: 10/37 = 0.2703...
H: (42/123) × 100 = 34.146...%
I: (18/43) × 100 = 41.860...%
J: 72 + 166 = 238

Now for the puzzle instruction: "To unlock puzzle four find the MEAN of all your answers."

So I need to find the mean of F, G, H, I, and J.

But wait - these are different types of numbers:
- F and G are relative frequencies (decimals between 0 and 1)
- H and I are percentages
- J is a count

This doesn't make sense to average together unless they're all converted to the same format. Let me reconsider...

Perhaps the answers should all be in decimal form:
- F: 24/35 ≈ 0.686
- G: 10/37 ≈ 0.270
- H: 34.15% = 0.3415
- I: 41.86% = 0.4186
- J: This is tricky - if it's 238, that's way larger than the others

Or maybe J refers only to the second survey total of 166?

Actually, rethinking J: "How many total people were in both surveys?" - Looking at just the second table, the grand total is 166. Perhaps "both surveys" here means the two groups (teachers and students) within that one survey? In that case, J = 166.

But 166 still doesn't fit well with the other answers for calculating a mean.

Let me try another interpretation: Maybe all answers should be expressed as decimals/fractions:
- F: 24/35
- G: 10/37
- H: 42/123 (not multiplied by 100)
- I: 18/43 (not multiplied by 100)
- J: Could this be 166/166 = 1? Or maybe it's asking for something else entirely?

Hmm, this is confusing. Let me just provide the answers as they naturally would be answered:

F: 24/35 or approximately 0.686
G: 10/37 or approximately 0.270
H: Approximately 34.1%
I: Approximately 41.9%
J: 238 (if combining both surveys) or 166 (if just the second survey)

Given the ambiguity with J and the mean calculation, let me provide the straightforward answers to each question.

Final Answer:
F: 24/35 (or 0.686)
G: 10/37 (or 0.270)
H: 34.1%
I: 41.9%
J: 238