erik is part of a dance group. for one month he kept a chart of the number of hours he participated in the three dance activities: lessons, practices, and dances.
dance activities
| | lessons | practices | dances |
|-------|---------|-----------|--------|
| week 1| 2 hours | 2 hours | 3 hours|
| week 2| 1 hour | 2 hours | 4 hours|
| week 3| 2 hours | 2 hours | 0 hours|
| week 4| 1 hour | 3 hours | 2 hours|
which question cannot be answered using the data in the table?
- which week did erik spend the least amount of time participating in all of the dance activities?
- that month, how many hours did erik average participating in dance lessons?
- that month, which dance activity did erik participate in the most?
- how many hours did erik average each month participating in dance practices?

Question

erik is part of a dance group. for one month he kept a chart of the number of hours he participated in the three dance activities: lessons, practices, and dances.
dance activities
|       | lessons | practices | dances |
|-------|---------|-----------|--------|
| week 1| 2 hours | 2 hours   | 3 hours|
| week 2| 1 hour  | 2 hours   | 4 hours|
| week 3| 2 hours | 2 hours   | 0 hours|
| week 4| 1 hour  | 3 hours   | 2 hours|
which question cannot be answered using the data in the table?
- which week did erik spend the least amount of time participating in all of the dance activities?
- that month, how many hours did erik average participating in dance lessons?
- that month, which dance activity did erik participate in the most?
- how many hours did erik average each month participating in dance practices?

Accepted Answer

To solve this, we analyze each option:

### Option 1: "Which week did Erik spend the least amount of time participating in all of the dance activities?"
- Calculate total hours per week:
  - Week 1: $2 + 2 + 3 = 7$ hours
  - Week 2: $1 + 2 + 4 = 7$ hours
  - Week 3: $2 + 2 + 0 = 4$ hours
  - Week 4: $1 + 3 + 2 = 6$ hours
- We can determine the week with the least total time (Week 3). So this question can be answered.

### Option 2: "That month, how many hours did Erik average participating in dance lessons?"
- Total lessons hours: $2 + 1 + 2 + 1 = 6$ hours
- Average = $\frac{6}{4} = 1.5$ hours. This question can be answered.

### Option 3: "That month, which dance activity did Erik participate in the most?"
- Total for each activity:
  - Lessons: $2 + 1 + 2 + 1 = 6$ hours
  - Practices: $2 + 2 + 2 + 3 = 9$ hours
  - Dances: $3 + 4 + 0 + 2 = 9$ hours
- Both Practices and Dances have 9 hours. Wait, but actually, we can still determine the top activities (even if tied). Wait, no—wait, the table is for one month (4 weeks). Wait, no, the question is "which dance activity did Erik participate in the most" for the month. We can calculate totals:
  - Lessons: $2 + 1 + 2 + 1 = 6$
  - Practices: $2 + 2 + 2 + 3 = 9$
  - Dances: $3 + 4 + 0 + 2 = 9$
  - So Practices and Dances are tied. But we can still identify the activities with the most (even if multiple). Wait, but maybe the issue is—no, wait, the fourth option:

### Option 4: "How many hours did Erik average each month participating in dance practices?"
- The data is for one month (4 weeks). To find the average "each month", we need data for multiple months. The table only has data for one month. So we can't find the average per month (since we need more than one month's data). Wait, no—wait, the question is "how many hours did Erik average each month participating in dance practices". But we only have one month's data. So we can't calculate an average over multiple months.

Wait, let's re-examine:

Wait, the first three options use the one - month (4 - week) data:

- Option 1: Uses weekly totals (from one month's data)
- Option 2: Uses one month's lessons data to find the average for that month (average per week in the month, but the question says "that month... average participating in dance lessons"—so average per week in the month? Wait, no, "average participating in dance lessons" for the month—probably average hours per week in the month, which we can calculate.

- Option 3: Uses one month's data to find total per activity.

- Option 4: "How many hours did Erik average each month participating in dance practices?" To find an average "each month", we need data from multiple months. The table only has data for one month. So we can't compute the average across multiple months.

Wait, but maybe I misread. Let's check the options again:

Wait, the fourth option: "How many hours did Erik average each month participating in dance practices?"

The data is for one month (4 weeks). To find the average "each month", we need to know the number of hours per month over multiple months. Since we only have one month's data, we can't calculate the average across months.

The other options:

- Option 1: We can calculate total hours per week (from the one - month data) and find the minimum.

- Option 2: We can calculate total lessons hours in the month and divide by 4 (number of weeks in the month) to get the average per week in the month (which is the average for the month's lessons).

- Option 3: We can calculate total hours for each activity in the month and compare.

So the question that cannot be answered is "How many hours did Erik average each month participating in dance practices?" because we need data from multiple months to find a monthly average, and we only have data for one month.

# Brief Explanations:
- For the first option, we can calculate total hours per week (e.g., Week 1: $2 + 2+3 = 7$, Week 2: $1 + 2 + 4=7$, Week 3: $2+2 + 0 = 4$, Week 4: $1+3 + 2 = 6$) and find the minimum.
- For the second option, total lessons hours: $2 + 1+2 + 1 = 6$, average is $\frac{6}{4}=1.5$ hours.
- For the third option, total for lessons: $6$, practices: $9$, dances: $9$ (we can identify the most - participated activities).
- For the fourth option, to find the average "each month" for dance practices, we need data from multiple months. Since we only have one month's data, we can't calculate this average.

# Answer:
How many hours did Erik average each month participating in dance practices?

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QUESTION IMAGE

Question

Explanation:

Option 1: "Which week did Erik spend the least amount of time participating in all of the dance activities?"

Option 2: "That month, how many hours did Erik average participating in dance lessons?"

Option 3: "That month, which dance activity did Erik participate in the most?"

Option 4: "How many hours did Erik average each month participating in dance practices?"

Answer:

	lessons	practices	dances
week 2	1 hour	2 hours	4 hours
week 3	2 hours	2 hours	0 hours
week 4	1 hour	3 hours	2 hours