Analyzing Two Way Frequency Tables - Binder Notes for Algebra 1 | TPT - Free Printable

Let’s go step by step to fill in the blanks correctly.

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First, look at the Two-Way Frequency Table:

We are given:

- 9th Graders: Sports = 128, No Sports = ? → Total = 205
→ So, No Sports for 9th Graders = 205 - 128 = 77

- 10th Graders: Sports = ?, No Sports = ? → Total = 219
→ We don’t have either yet — we’ll come back.

- 11th Graders: Sports = 119, No Sports = 86 → Total = 119 + 86 = 205

- 12th Graders: Sports = ?, No Sports = 103 → Total = 185
→ So, Sports for 12th Graders = 185 - 103 = 82

Now, let’s find totals for columns:

Total Sports column:
= 128 (9th) + ? (10th) + 119 (11th) + 82 (12th)
But we also know from the bottom row: “Two-Way Frequency Table” total is 814.

Also, Total No Sports column:
= 77 (9th) + ? (10th) + 86 (11th) + 103 (12th)

And total students = 814.

So, sum of all row totals should be 814:

Row totals given:
9th: 205
10th: 219
11th: 205
12th: 185
Sum = 205 + 219 + 205 + 185 = let’s calculate:

205 + 219 = 424
424 + 205 = 629
629 + 185 = 814 ✔ Good.

Now, column totals:

Sports column total = 128 + x + 119 + 82 = (128+119+82) + x = 329 + x

No Sports column total = 77 + y + 86 + 103 = (77+86+103) + y = 266 + y

And total = 814 → so (329 + x) + (266 + y) = 814
→ 595 + x + y = 814
→ x + y = 219 → which matches the 10th grade total! So that checks out.

But we need actual numbers for 10th graders.

Wait — actually, we can get the column totals another way.

Total Sports = sum of sports across grades = 128 + ? + 119 + 82

We don’t have 10th grade sports yet. But maybe we can find it from the marginal frequency definition?

Actually, let’s move to the definitions first — they’re conceptual.

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Definitions Section:

> Two-Way Frequency Table: Shows the relationship between two sets of ___ data.

Answer: categorical — because we’re grouping by grade level and participation (sports/no sports), both categories.

> Joint Frequency: Entries in the ___.

Looking at context — joint frequencies are the inner cells (like 128, 77, etc.), not the totals. So: interior cells or body of the table. But standard term: cells that are not in the total row or column → often called “joint frequencies” are the counts inside, excluding margins.

Standard answer: inside the table (not including totals) → but blank says “Entries in the ___.” Probably: cells

But let’s check common textbook phrasing.

Actually, typical definition:
Joint frequency = count in a specific cell (e.g., 9th graders who play sports).
Marginal frequency = total for a row or column.

So:

> Joint Frequency: Entries in the cells (or “interior”) — but most likely expected answer: cells

Wait — looking at next line:

> Marginal Frequency: Entries in the ___ column or row of the table.

That would be total column or row.

Yes!

So:

- Joint Frequency: Entries in the cells (meaning the non-total parts)
- Marginal Frequency: Entries in the total column or row

But sometimes “marginal” refers to the edge — so “margin” — but here it says “___ column or row”, so likely “total”.

Confirming with standard math curriculum:

In two-way tables:
- Joint frequencies: the values inside the table (not on the edges)
- Marginal frequencies: the row and column totals (on the margins)

So:

> Joint Frequency: Entries in the interior or body? But blank probably expects: cells

Actually, many textbooks say: “Joint frequencies are the entries in the body of the table.”

But since the next one says “column or row”, perhaps:

Let me think differently.

Perhaps:

“Joint Frequency: Entries in the table” — too vague.

Wait — look at the structure:

It says:

Two-Way Frequency Table: Shows the relationship between two sets of ___ data. → categorical

Joint Frequency: Entries in the ___. → This is ambiguous, but in context, since marginal is defined as total row/column, joint must be the other ones → so non-total cells or just cells

But I recall a standard phrase: “Joint frequencies are found in the cells of the table that are not in the total row or column.”

For simplicity, and based on common worksheets, the answer is often:

Joint Frequency: Entries in the cells

Marginal Frequency: Entries in the total column or row

Yes.

Then conditional relative frequency later.

Now, Two-Way Relative Frequency Table section:

> Two-Way Relative Frequency Table: Shows the relationship between two sets of ___ data using ___ instead of raw counts.

First blank: again categorical

Second blank: relative frequencies or percentages or proportions

Typically: relative frequencies (which can be decimals or percents)

But the sentence says “using ___ instead of raw counts” → so relative frequencies

Then:

> Joint Relative Frequency: The ___ of the joint frequency to the total.

→ ratio

> Marginal Relative Frequency: The ___ of the marginal frequency to the total.

→ ratio

> Conditional Relative Frequency: The ___ of the joint frequency to the related marginal frequency.

→ ratio

All these are ratios.

Sometimes specified as decimal or percent, but “ratio” is correct.

Now, back to filling the table numerically.

We had:

9th Graders: Sports=128, No Sports=77, Total=205

11th Graders: Sports=119, No Sports=86, Total=205

12th Graders: Sports=82, No Sports=103, Total=185

10th Graders: Total=219, Sports=?, No Sports=?

Total Sports column = 128 + S10 + 119 + 82 = 329 + S10

Total No Sports = 77 + N10 + 86 + 103 = 266 + N10

And S10 + N10 = 219

Also, total overall = 814

So 329 + S10 + 266 + N10 = 814 → 595 + (S10 + N10) = 814 → 595 + 219 = 814 ✔

But we still need S10 and N10 individually.

Wait — is there more info? The problem doesn't give them directly. Maybe we don't need to fill the table numerically for the blanks? Let's read the task again.

The user uploaded an image with blanks to fill in the definitions and possibly the table, but the instruction is to solve the problem — which seems to be filling the blanks in the text, not necessarily computing missing table values unless required.

Looking at the worksheet layout:

There are blanks in the definition sentences.

Specifically:

Under "Two-Way Frequency Table":

Shows the relationship between two sets of ___ data. → categorical

Joint Frequency: Entries in the ___. → cells (or perhaps "interior", but "cells" is simpler)

Marginal Frequency: Entries in the ___ column or row of the table. → total

Then under "Two-Way Relative Frequency Table":

Shows the relationship between two sets of ___ data using ___ instead of raw counts. → categorical, relative frequencies

Joint Relative Frequency: The ___ of the joint frequency to the total. → ratio

Marginal Relative Frequency: The ___ of the marginal frequency to the total. → ratio

Conditional Relative Frequency: The ___ of the joint frequency to the related marginal frequency. → ratio

These are standard terms.

To confirm:

- Categorical data: yes, grade level and sports participation are categories.

- Joint frequency: the count in each cell (e.g., 128 is joint frequency for 9th grade and sports)

- Marginal frequency: the row or column totals (e.g., 205 for 9th grade total)

- Relative frequencies: proportions or percentages of the total

- Ratios: since relative frequency = part / whole

So all blanks should be filled as above.

Now, about the table itself — the worksheet has empty cells, but the question might only require filling the definition blanks, as those are explicitly written with underscores.

Since the user said "solve the problem accurately" and the main content is the definitions with blanks, I'll focus on those.

But to be thorough, let's see if any numerical values are needed for the blanks — no, the blanks are all in the definition sentences.

So final answers for blanks:

1. categorical
2. cells
3. total
4. categorical
5. relative frequencies
6. ratio
7. ratio
8. ratio

But let's write them in order as they appear.

From top to bottom:

First blank: "two sets of ___ data" → categorical

Second: "Entries in the ___." → cells

Third: "Entries in the ___ column or row" → total

Fourth: "two sets of ___ data" → categorical

Fifth: "using ___ instead of raw counts" → relative frequencies

Sixth: "The ___ of the joint frequency to the total" → ratio

Seventh: "The ___ of the marginal frequency to the total" → ratio

Eighth: "The ___ of the joint frequency to the related marginal frequency" → ratio

Yes.

Some might argue for "proportion" instead of "ratio", but in this context, "ratio" is commonly used in middle/high school stats for relative frequency definitions.

Also, for joint frequency, some sources say "the interior cells" but "cells" is sufficient and matches the level.

Final Answer:

categorical, cells, total, categorical, relative frequencies, ratio, ratio, ratio