Question

part b
indicate whether each value or description represents a joint frequency or a marginal frequency.

value or description	joint frequency	marginal frequency
number of sophomores	○	○
80	○	○
number of freshmen who selected raffle	○	○
number of students who selected car wash	○	○
29	○	○
number of students who selected bake sale who were sophomores	○	○

Explanation:

Step1: Recall Definitions

- **Joint Frequency**: Frequency for a specific combination of two categories (e.g., freshmen who selected raffle, sophomores who selected bake sale).
- **Marginal Frequency**: Frequency for a single category (e.g., total sophomores, total students who selected car wash).

Step2: Analyze Each Entry

1. **"23"**: Assume it's a joint or marginal. If it's a single category (e.g., a total), but likely joint? Wait, no—wait, let's check others. Wait, the table has entries:
- "Number of sophomores": Marginal (single category: sophomores).
- "80": Marginal (total, as per the hand).
- "Number of freshmen who selected raffle": Joint (combination of freshmen and raffle).
- "Number of students who selected car wash": Marginal (single category: car wash).
- "29": Let's see the last entry: "Number of students who selected bake sale who were sophomores"—joint (combination of bake sale and sophomores).

Wait, let's go step by step for each row:

1. **Row 1: "23"**
Need context, but likely a joint or marginal. Wait, maybe "23" is a joint (e.g., a combination). But let's use definitions.
- Joint: combination of two variables (class + activity).
- Marginal: single variable (class or activity).

2. **Row 2: "Number of sophomores"**
Marginal (single category: sophomores) → select Marginal Frequency.

3. **Row 3: "80"**
As per the hand, it's Marginal (total, so single category) → select Marginal Frequency.

4. **Row 4: "Number of freshmen who selected raffle"**
Joint (freshmen + raffle) → select Joint Frequency.

5. **Row 5: "Number of students who selected car wash"**
Marginal (single category: car wash) → select Marginal Frequency.

6. **Row 6: "29"**
Likely a joint (e.g., a combination). Wait, the last entry: "Number of students who selected bake sale who were sophomores" → joint (bake sale + sophomores) → select Joint Frequency.

Wait, but the problem is to indicate for each. Let's structure each:

- **"23"**: If it's a joint (e.g., a combination), but without more, but let's assume. Wait, maybe the first "23" is a joint (e.g., a class-activity combo). But let's use the definitions:

Let's list each:

1. **"23"**:
- If it's a combination (e.g., juniors who selected something), joint. So Joint Frequency.

2. **"Number of sophomores"**:
- Single category (sophomores), Marginal Frequency.

3. **"80"**:
- Single category (total, e.g., total students), Marginal Frequency (as per the hand).

4. **"Number of freshmen who selected raffle"**:
- Combination (freshmen + raffle), Joint Frequency.

5. **"Number of students who selected car wash"**:
- Single category (car wash), Marginal Frequency.

6. **"29"**:
- Combination (bake sale + sophomores), Joint Frequency.

7. **"Number of students who selected bake sale who were sophomores"**:
- Combination (bake sale + sophomores), Joint Frequency.

But the table has checkboxes. Let's map each:

- **"23"**: Joint Frequency (circle under Joint)
- **"Number of sophomores"**: Marginal Frequency (circle under Marginal)
- **"80"**: Marginal Frequency (circle under Marginal, as per the hand)
- **"Number of freshmen who selected raffle"**: Joint Frequency (circle under Joint)
- **"Number of students who selected car wash"**: Marginal Frequency (circle under Marginal)
- **"29"**: Joint Frequency (circle under Joint)
- **"Number of students who selected bake sale who were sophomores"**: Joint Frequency (circle under Joint)

But the problem is to indicate for each. Let's present each:

1. **"23"**: Joint Frequency
2. **"Number of sophomores"**: Marginal Frequency
3. **"80"**: Marginal Frequency
4. **"Number of freshmen who selected raffle"**: Joint Frequency
5. **"Number of students who selected car wash"**: Marginal Frequency
6. **"29"**: Joint Frequency
7. **"Number of students who selected bake sale who were sophomores"**: Joint Frequency

But since the user's table has these entries, we need to mark each. Let's do each row:

- Row 1 (Value: 23): Joint Frequency (circle Joint)
- Row 2 (Description: Number of sophomores): Marginal Frequency (circle Marginal)
- Row 3 (Value: 80): Marginal Frequency (circle Marginal, as per the hand)
- Row 4 (Description: Number of freshmen who selected raffle): Joint Frequency (circle Joint)
- Row 5 (Description: Number of students who selected car wash): Marginal Frequency (circle Marginal)
- Row 6 (Value: 29): Joint Frequency (circle Joint)
- Row 7 (Description: Number of students who selected bake sale who were sophomores): Joint Frequency (circle Joint)

But maybe the user wants the selection for each. Let's confirm with definitions:

- Joint Frequency: frequency of a cell (combination of two variables).
- Marginal Frequency: frequency of a row total or column total (single variable).

So:

- "Number of sophomores": Marginal (row/column total for sophomores).
- "Number of freshmen who selected raffle": Joint (cell frequency: freshmen ∩ raffle).
- "Number of students who selected car wash": Marginal (row/column total for car wash).
- "Number of students who selected bake sale who were sophomores": Joint (cell frequency: sophomores ∩ bake sale).
- "23", "80", "29": These are the numerical values of the frequencies. So "23"—if it's a cell (joint), "80"—row/column total (marginal), "29"—cell (joint).

So for each:

1. **"23"**: Joint Frequency (circle Joint)
2. **"Number of sophomores"**: Marginal Frequency (circle Marginal)
3. **"80"**: Marginal Frequency (circle Marginal)
4. **"Number of freshmen who selected raffle"**: Joint Frequency (circle Joint)
5. **"Number of students who selected car wash"**: Marginal Frequency (circle Marginal)
6. **"29"**: Joint Frequency (circle Joint)
7. **"Number of students who selected bake sale who were sophomores"**: Joint Frequency (circle Joint)

But since the table has radio buttons, we mark each:

- For "23": Joint Frequency (select the circle under Joint)
- For "Number of sophomores": Marginal Frequency (select the circle under Marginal)
- For "80": Marginal Frequency (select the circle under Marginal)
- For "Number of freshmen who selected raffle": Joint Frequency (select the circle under Joint)
- For "Number of students who selected car wash": Marginal Frequency (select the circle under Marginal)
- For "29": Joint Frequency (select the circle under Joint)
- For "Number of students who selected bake sale who were sophomores": Joint Frequency (select the circle under Joint)

But maybe the user wants the answers for each. Let's summarize:

- "23": Joint
- "Number of sophomores": Marginal
- "80": Marginal
- "Number of freshmen who selected raffle": Joint
- "Number of students who selected car wash": Marginal
- "29": Joint
- "Number of students who selected bake sale who were sophomores": Joint

But the problem is to "indicate whether each value or description represents a joint frequency or a marginal frequency"—so for each row, select Joint or Marginal.

Let's do each:

1. **Value: 23**
Joint Frequency (because it's likely a combination of class and activity, not a total).

2. **Description: Number of sophomores**
Marginal Frequency (total for the "sophomores" category, not a combination).

3. **Value: 80**
Marginal Frequency (total for a category, as indicated by the hand).

4. **Description: Number of freshmen who selected raffle**
Joint Frequency (combination of "freshmen" and "selected raffle").

5. **Description: Number of students who selected car wash**
Marginal Frequency (total for the "selected car wash" category).

6. **Value: 29**
Joint Frequency (combination of "students who selected bake sale" and "were sophomores").

7. **Description: Number of students who selected bake sale who were sophomores**
Joint Frequency (combination of two categories: bake sale and sophomores).

Answer:

• For "23": Joint Frequency (select the circle under "Joint Frequency")
• For "Number of sophomores": Marginal Frequency (select the circle under "Marginal Frequency")
• For "80": Marginal Frequency (select the circle under "Marginal Frequency")
• For "Number of freshmen who selected raffle": Joint Frequency (select the circle under "Joint Frequency")
• For "Number of students who selected car wash": Marginal Frequency (select the circle under "Marginal Frequency")
• For "29": Joint Frequency (select the circle under "Joint Frequency")
• For "Number of students who selected bake sale who were sophomores": Joint Frequency (select the circle under "Joint Frequency")