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It appears you've uploaded two images related to a statistics problem involving the distribution of students' heights, as well as questions about calculating the mean and median of their distances when standing on a platform.

### Given Data
- The dataset is based on the height of 25 students in Mrs. Nataro’s class, as shown in the dotplot and the table summary:
  - \( n = 25 \) (Number of students)
  - \( \bar{x} = 67 \) (Mean height in inches)
  - \( s_x = 4.29 \) (Standard deviation)
  - Minimum = 60 inches
  - Q1 = 63 inches
  - Median = 66 inches
  - Q3 = 70 inches
  - Maximum = 75 inches

### Problem Context
The students are standing on a 6-inch-high platform. You are asked to find the **mean** and **median** of the distances measured from the **top of their heads to the ground**.

### Key Idea
The distances measured from the top of their heads to the ground would be their **height minus 6 inches**, because they are standing on a platform that raises their height by 6 inches. Thus, the transformed data for their height would subtract 6 from each value in the dataset.

### Solution Approach

1. **Mean of the Distribution of Distances:**
   - To find the mean of the new distribution, you subtract 6 inches from the original mean height:
   \[
   \text{New Mean} = \bar{x} - 6 = 67 - 6 = 61 \text{ inches}
   \]
   Therefore, the new mean is **61 inches**. The answer "61" that was previously marked incorrect seems to be correct.

2. **Median of the Distribution of Distances:**
   - Similarly, to find the median of the new distribution, you subtract 6 inches from the original median height:
   \[
   \text{New Median} = \text{Median} - 6 = 66 - 6 = 60 \text{ inches}
   \]
   Therefore, the new median is **60 inches**, not 66 as indicated in the incorrect answer.

### Conclusion
- **Mean of distances:** 61 inches (correct)
- **Median of distances:** 60 inches (correction needed)

Would you like further details on how these calculations work, or do you have additional questions?

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**Related Questions:**

1. How does subtracting or adding a constant affect measures like the mean and median?
2. How does this transformation affect the standard deviation of the distribution?
3. What are Q1 and Q3 in the new distribution of distances?
4. How would the range of the dataset change after subtracting 6 inches?
5. How would this scenario change if the platform height were not constant for all students?

**Tip:** When a constant is added or subtracted from every value in a dataset, it shifts the mean and median by that same constant, but the spread (like standard deviation) remains unchanged.

Suppose that Mrs. Nataro has the entire class stand on a 6-inch-high platform and then asks the students to measure the distance from the top of their heads to the ground.

Learn how to calculate the mean and median after subtracting a constant from a dataset. This example uses heights of students in Mrs. Nataro's class, focusing on descriptive statistics. Suitable for students in Grades 9-11.

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