Math worksheet with three problems analyzing sample data to infer population characteristics.

Here are the solutions to the problems on the worksheet.

Problem 1

Question: Based on the information presented can you infer anything about the relationship between the number of nails, screws and bolts in the bucket?

Step-by-step Solution:
1. Look at the data for Nails: The numbers are 19, 18, 19, 19, 18, 20, 22. Most of these numbers are around 19.
2. Look at the data for Screws: The numbers are 20, 19, 20, 22, 20, 20, 21. These numbers are very close to the nail numbers, mostly around 20.
3. Look at the data for Bolts: The numbers are 19, 20, 21, 21, 21, 21, 22. These are also very similar, mostly around 21.
4. Compare them: In every single sample (Sample #1 through #7), the counts for all three items are almost identical. For example, in Sample #1, they are 19, 20, and 19. In Sample #6, they are 20, 20, and 21.
5. Conclusion: Since the carpenter grabbed random handfuls and got roughly the same amount of each item every time, it is safe to guess that there are about the same number of nails, screws, and bolts in the whole bucket.

Final Answer:
Yes, you can infer that there are approximately equal amounts of nails, screws, and bolts in the bucket because the counts in every sample were very close to each other.

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Problem 2

Question: Based on the information presented can you infer anything about the types of cans donated?

Step-by-step Solution:
1. Look at Sample #1: There were 4 peas, 5 carrots, and 3 green beans. Carrots were the highest here.
2. Look at Sample #2: There were 3 peas, 3 carrots, and 4 green beans. Green beans were the highest here.
3. Compare the totals:
* Total Peas: $4 + 3 = 7$
* Total Carrots: $5 + 3 = 8$
* Total Green Beans: $3 + 4 = 7$
4. Analyze the pattern: The numbers are all very small and close together (3, 4, or 5 per sample). Unlike the first problem where one type might have been clearly larger, here the amounts fluctuate. One sample had more carrots, the other had more green beans.
5. Conclusion: Because the numbers are so close and switch back and forth, we can infer that the donation box likely contains a fairly even mix of all three vegetables, or that the distribution is random with no single vegetable being significantly more common than the others.

Final Answer:
Yes, you can infer that the types of cans donated are distributed relatively evenly. There is no strong evidence that one specific vegetable was donated much more frequently than the others, as the counts in the samples are very similar.

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Problem 3

Question: Based on the information presented can you infer anything about the types of books donated?

Step-by-step Solution:
1. Look at the "Fiction" row: The numbers are 62, 61, 59, 59, 58, 60. Every single number is high, staying consistently around 60.
2. Look at the "Non-Fiction" row: The numbers are 52, 54, 50, 54, 54, 50. Every single number is lower, staying consistently around 50 to 54.
3. Compare the two rows: In every single sample (1 through 6), the number of Fiction books is higher than the number of Non-Fiction books.
* Sample 1: $62 > 52$
* Sample 2: $61 > 54$
* Sample 3: $59 > 50$
* ...and so on.
4. Conclusion: Since Fiction books appeared more often in every single handful the librarian pulled, it is highly likely that there are more Fiction books in the entire donation box than Non-Fiction books.

Final Answer:
Yes, you can infer that there are more Fiction books in the donation box than Non-Fiction books. In every sample taken, the count for Fiction books was consistently higher than the count for Non-Fiction books.