Which of the following statements are true about the boxplot shown here?
I. The distribution is skewed right.
II. The interquartile range is about 8.
III. The median is about 10.
I only
II only
III only
I and II
II and III

To determine which of the statements are true about the boxplot, let's analyze each statement:

**I. The distribution is skewed right.**
- A right-skewed distribution means that the tail on the right side of the boxplot is longer than the tail on the left side. This would typically show a longer whisker on the right side of the box, and the median would be closer to the left side of the box.

**II. The interquartile range is about 8.**
- The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). By observing the box in the boxplot, you can estimate the IQR by subtracting Q1 from Q3.

**III. The median is about 10.**
- The median is represented by the line inside the box. You can estimate its value by looking at the position of this line.

Without the actual boxplot, we cannot definitively answer these questions, but here's how to approach them:

- If the boxplot shows a longer right whisker and the median is not centered but shifted to the left, statement I would be true.
- To determine if the IQR is about 8, you need to estimate the values of Q1 and Q3 from the boxplot.
- To assess whether the median is about 10, look at where the line inside the box is positioned.

### Logical Approach:
- **I only** would be correct if only the distribution is skewed right.
- **II only** would be correct if only the IQR is approximately 8.
- **III only** would be correct if only the median is about 10.
- **I and II** would be correct if both the distribution is skewed right and the IQR is about 8.
- **II and III** would be correct if both the IQR is about 8 and the median is about 10.

You can check the boxplot against these criteria to find the correct answer. If you're able to provide the boxplot or describe it in more detail, I can give you a more specific answer.

Would you like more details or have any questions? Here are five related questions:

1. How can you determine the skewness of a distribution from a boxplot?
2. What are the key components of a boxplot, and what do they represent?
3. How is the interquartile range calculated from a boxplot?
4. Why is the median important in summarizing data, and how does it relate to the mean?
5. How do outliers appear on a boxplot, and how can they affect the analysis?

**Tip:** When analyzing boxplots, always pay close attention to the whiskers and the position of the median to quickly assess the skewness and spread of the data.

Learn how to analyze a boxplot by determining skewness, calculating the interquartile range (IQR), and estimating the median. This problem covers key statistical concepts like data distribution, skewness, and median position. Suitable for students in Grades 6-8.

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