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From the box and whisker plot provided, we can address the following:

1. **Range of the Data:**
   The range is calculated as the difference between the highest and lowest values in the dataset. Here, the lowest value is 12 and the highest is 74. Thus, the range is \( 74 - 12 = 62 \).

2. **Position of the Two Middle Groups Relative to the Median:**
   The box plot shows the median as the line within the box (between Q2 and Q3), which appears to be around the mid-40s. The middle groups, as indicated by Q2 and Q3 (which enclose the median), are spread from approximately 30 to 60. To determine if these groups are more spread out above or below the median, we can look at the interquartile range (IQR), which is the difference between Q3 and Q1:
   - \( Q1 \) (First quartile) is approximately at 30.
   - \( Q3 \) (Third quartile) is approximately at 60.
   - IQR = \( 60 - 30 = 30 \).

   Since the median (around 45) divides the IQR into two halves (approximately 15 units each from Q2 to the median and from the median to Q3), both middle groups are equally spread around the median. However, if we consider the entire dataset, it's clear that the data points (12, 23) below Q1 and (74) above Q3 are more dispersed than the middle groups relative to the median, especially the value 74, which is a significant outlier.

Thus, the answer to whether the two middle groups are more spread out above or below the median is "Neither"; they are similarly spread around the median.

If you need further clarification or have additional questions, feel free to ask! Here are some related questions you might consider:

1. What do Q1, Q2, and Q3 represent in a box plot?
2. How can outliers affect the interpretation of a box plot?
3. What additional information can be derived from analyzing the whiskers of a box plot?
4. How does the range compare to the interquartile range in terms of data spread?
5. Can we calculate the exact value of the median from this box plot?

**Tip:** When analyzing a box plot, always check for outliers as they can significantly influence the mean and range, providing deeper insights into the data distribution.

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

Analyze a box and whisker plot to calculate the range and determine if the data in the middle groups is more spread above or below the median. This problem covers key concepts like range, median, and interquartile range, suitable for Grades 6-8.

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