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### Boxplot Analysis:
- The boxplots represent Set A and Set B with respect to a number line (horizontal axis).
- The key features of boxplots:
  - The central box shows the interquartile range (IQR), from the 1st quartile (Q1) to the 3rd quartile (Q3).
  - The line inside the box represents the median (Q2).
  - The "whiskers" extend to the minimum and maximum values (within a certain range).

### Statement Analysis:

1. **Statement I: "Set A contains more data than Set B."**
   - **False**: Boxplots do not indicate the number of data points, only the spread and distribution. The amount of data cannot be inferred from the size of the boxplot. Both sets could contain the same number of data points.

2. **Statement II: "The box of Set A contains more data than the box of Set B."**
   - **False**: The size of the box shows the interquartile range (IQR), but it does not indicate more data points inside the box. Again, this relates to the distribution, not the amount of data.

3. **Statement III: "The data in Set A have a larger range than the data in Set B."**
   - **True**: The range of a dataset is the difference between the maximum and minimum values. From the boxplots, it is clear that Set A has a wider overall spread compared to Set B, as its whiskers extend farther than those of Set B.

### Correct Answer:
The only correct statement is **III**, so the answer is **B) III only**.

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Would you like more details about boxplot analysis or another concept? Here are some additional related questions:

1. What is the interquartile range (IQR) and how is it calculated?
2. How do boxplots help in identifying outliers?
3. How does the range differ from the interquartile range?
4. Can boxplots show skewness in the data?
5. How do you calculate the mean and median from a boxplot?

**Tip**: Always remember, boxplots only provide information about the spread and distribution of data, not the number of data points.

The boxplots above summarize two data sets, A and B. Which of the following must be true? 
 I. Set A contains more data than Set B. 
 II. The box of Set A contains more data than the box of Set B. 
 III. The data in Set A have a larger range than the data in Set B.

Analyze and interpret boxplots of data sets A and B to determine the relationship between data range, distribution, and overall spread. This example explores the difference in the range of two sets. Suitable for high school students.

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