https://file.aiquickdraw.com/mathbot/file/1726900310676o5pkz2jo.jpg

From the box-and-whisker plot provided in the image, we can extract the following details:

- Minimum value (left whisker): 3.9
- Maximum value (right whisker): 71.7
- First quartile (Q1): 19.3
- Median (Q2): 32.1
- Third quartile (Q3): 57.6

### 1. **Range of the data**:
The range is the difference between the maximum and minimum values.

\[
\text{Range} = 71.7 - 3.9 = 67.8
\]

### 2. **Spread of the two middle groups**:
The "two middle groups" likely refer to the interquartile range (IQR), which is the spread between Q1 and Q3.

\[
\text{IQR} = Q3 - Q1 = 57.6 - 19.3 = 38.3
\]

Now, let's answer the second part of the question: "Are the numbers in the two middle groups more spread out above or below the median?"

- The spread **below the median** (Q2 - Q1): 
  \[
  32.1 - 19.3 = 12.8
  \]
  
- The spread **above the median** (Q3 - Q2): 
  \[
  57.6 - 32.1 = 25.5
  \]

So, the numbers above the median are more spread out than those below the median.

### Summary of answers:
- **Range**: 67.8
- **The numbers are more spread out above the median.**

Would you like more details on any part? Here are some related questions to explore further:

1. What is the significance of the interquartile range (IQR)?
2. How does the median split the dataset, and why is it useful in statistics?
3. What can the whiskers in a box plot tell us about potential outliers?
4. How is the range different from the IQR in terms of data analysis?
5. What does a wider spread above the median suggest about the distribution?

**Tip:** The range gives a sense of the overall spread, but the interquartile range is more robust to outliers!

What is the range of this data? Are the numbers in the two middle groups more spread out above or below the median?

Explore how to calculate the range and interquartile range (IQR) using a box-and-whisker plot. Understand the spread of data points around the median and how to determine if they are more spread out above or below the median. This example walks through data analysis step by step, ideal for students in Grades 6-9.

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