D. Why would the data sets appear to have similar spreads using interquartile range and very different spreads using the range? Choose the best answer. The different medians make the range greater. The clusters make the range greater. The outliers make the range greater. The lower quartiles make the range greater. The upper quartiles make the range greater.

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UpStudy AI · Accepted Answer

The best answer is:

**The outliers make the range greater.**

**Explanation:**

- **Interquartile Range (IQR):** Measures the spread of the middle 50% of the data, specifically between the first quartile (25th percentile) and the third quartile (75th percentile). It is resistant to outliers and provides a consistent measure of spread for the central portion of the data.

- **Range:** Measures the total spread of the data from the minimum to the maximum value. It is highly sensitive to outliers since extreme values can significantly increase the range.

If two data sets have similar IQRs but very different ranges, it suggests that while their central distributions are similar, one or both of the data sets contain outliers that extend the range. These outliers do not affect the IQR but do make the overall range appear much larger.

**Incorrect Options:**

1. **Different medians:** Medians affect the central tendency, not the spread.
2. **Clusters:** While clusters can affect the distribution, they don't directly explain a large difference in ranges if IQRs are similar.
3. **Lower quartiles:** The IQR already accounts for both lower and upper quartiles. Differences here would affect the IQR.
4. **Upper quartiles:** Similar to lower quartiles, differences would affect the IQR.

**Final Answer:**  
The outliers make the range greater.
Outliers make the range greater.

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