A group of adult males has foot lengths with a mean of 27.45 cm and a standard deviation of 1.23 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 30.3 cm significantly low or significantly​ high? Explain.

The **range rule of thumb** is a simple method to estimate the significant limits of data values based on the mean and standard deviation. It suggests that significant values are typically located more than two standard deviations away from the mean.

To identify the limits of significant values, we follow these steps:

1. **Lower limit** (significantly low):  
   \[
   \text{Lower limit} = \text{Mean} - 2 \times \text{Standard deviation}
   \]
   \[
   \text{Lower limit} = 27.45 - 2 \times 1.23 = 27.45 - 2.46 = 24.99 \, \text{cm}
   \]

2. **Upper limit** (significantly high):  
   \[
   \text{Upper limit} = \text{Mean} + 2 \times \text{Standard deviation}
   \]
   \[
   \text{Upper limit} = 27.45 + 2 \times 1.23 = 27.45 + 2.46 = 29.91 \, \text{cm}
   \]

### Interpretation:

- **Values below 24.99 cm** are considered significantly low.
- **Values above 29.91 cm** are considered significantly high.

Now, let's evaluate whether a foot length of **30.3 cm** is significantly high:

Since 30.3 cm is greater than the upper limit of 29.91 cm, this value is **significantly high** according to the range rule of thumb.

### Summary:

- **Lower limit (significantly low)**: 24.99 cm
- **Upper limit (significantly high)**: 29.91 cm
- A foot length of **30.3 cm** is significantly high because it exceeds 29.91 cm.

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Would you like more details or have any questions? Here are some additional questions for deeper understanding:

1. How is the range rule of thumb different from other significance tests?
2. What are other methods to determine if values are significantly high or low?
3. How is the standard deviation used in determining significant limits?
4. Can we use this method for non-normal distributions?
5. What are the limitations of the range rule of thumb?

**Tip**: The range rule of thumb is a quick estimate, but it may not be as precise as methods like z-scores or hypothesis testing, especially for skewed data distributions.

A group of adult males has foot lengths with a mean of 27.45 cm and a standard deviation of 1.23 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 30.3 cm significantly low or significantly high? Explain.

Understand how to use the range rule of thumb to identify significantly high or low foot lengths. For adult males, with a mean foot length of 27.45 cm and a standard deviation of 1.23 cm, learn how to determine whether a foot length of 30.3 cm is significantly high.

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