Is 60 years significantly high using the Range Rule of Thumb? The standard deviation is 9.6 years.

The **Range Rule of Thumb** is a quick way to estimate the range of a data set. It suggests that most data values fall within **four standard deviations** of the mean, specifically within the range:

\[
\text{Range} = \mu \pm 2\sigma
\]

Where:
- \(\mu\) is the mean (average) of the data.
- \(\sigma\) is the standard deviation.

Since you're asking about the value **60 years** in relation to this rule, we need the mean (\(\mu\)) to accurately apply it. However, without the mean, we can use the standard deviation you provided (\(\sigma = 9.6\)) to get a sense of how far **60 years** might be from the mean.

### Steps:
1. The typical range would be \(\mu \pm 2(9.6)\), or \(\mu \pm 19.2\).
2. Compare **60 years** to this range:
   - If 60 years is within this range, it's not significantly high.
   - If 60 years falls outside of this range, it would be considered significantly high (or low, depending on the context).

To summarize:
- If we knew the mean, we could clearly assess whether 60 years is significantly high. However, if the mean were in a typical range (say 40–50 years), then **60 years could be above the expected range**, making it somewhat high.

Would you like to provide the mean to calculate more precisely?

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Here are 5 related questions to extend this understanding:
1. What is the mean value in this data set for better assessment?
2. How do you interpret the Range Rule of Thumb in practice?
3. How can outliers affect the application of this rule?
4. What are other methods to check if a value is significantly high?
5. Can the Range Rule of Thumb be applied to non-normally distributed data?

**Tip**: When using the Range Rule of Thumb, make sure your data follows a roughly normal distribution for accurate results.

Learn how to determine if 60 years is significantly high using the Range Rule of Thumb, with a standard deviation of 9.6 years. This problem covers key statistical concepts, including the Range Rule of Thumb and how to apply it with standard deviation. Suitable for students in Grades 9-12.

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