Sampling Techniques Themed Math Worksheets | Ages 11-13 - Free Printable

Let's solve each part of the problem step by step, explaining the difference between population and sample:

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🔹 Definitions:

- Population: The entire group that you are interested in studying.
- Sample: A subset (a smaller part) of the population that is selected to represent the whole.

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✔ Problem 1: Books in the Library

> Image:
> - Left: 10 books on a shelf
> - Right: All books in the library

Question:
Identify which is the population and which is the sample.

#### ✔ Answer:
- Population: All books in library
- Sample: 10 books in library

#### 📝 Explanation:
The entire collection of books in the library is the population. The 10 books are just a portion of that collection — so they are a sample.

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✔ Problem 2: Survey of 3512 Middle School Children

> A survey of 3512 middle school children found that 27% could be classified as advanced learners. Is it a population or sample?

#### ✔ Answer:
Sample

#### 📝 Explanation:
Even though 3512 is a large number, this is not every middle school child (which would be the population). It’s a subset of all middle school children being studied. So, it's a sample.

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✔ Problem 3: Average Height at Boutique

> The average height of every person entering the fashion boutique in a city within 4 hours was 5’5”. Is it a population or sample?

#### ✔ Answer:
Population

#### 📝 Explanation:
The key word here is "every person" who entered the boutique during that time. Since it includes all individuals in that specific group (within the 4-hour window), it represents the entire group of interest, so it's a population.

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✔ Problem 4: Harvard University Students

> Select 100 students currently enrolled at Harvard University and ask how old they are and if they live nearby.

#### ✔ Answer:
- Population: All students currently enrolled at Harvard University
- Sample: 100 students selected from Harvard University

#### 📝 Explanation:
The population is the entire group of interest — all Harvard students. The sample is the smaller group of 100 students chosen to represent the larger population.

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✔ Final Answers Summary:

| Question | Population | Sample |
|--------|------------|--------|
| 1 | All books in library | 10 books in library |
| 2 | N/A | Sample |
| 3 | N/A | Population |
| 4 | All students currently enrolled at Harvard University | 100 selected students |

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💡 Key Takeaway:
Always ask: *"Is this the entire group of interest, or just a part?"*
- If it's all, it's a population.
- If it's some, it's a sample.

✔ Done! Let me know if you'd like a printable version or visual aid!