Estimating Standard Deviation with the Range Rule of Thumb. In Exercises 29–32, refer to the data in the indicated exercise. After finding the range of the data, use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the standard deviation computed using all of the data.


Body Temperatures Refer to Data Set 5 “Body Temperatures” in Appendix B and use the body temperatures for 12:00 AM on day 2.

Verified step by step guidance

1. Step 1: Identify the range of the data. The range is calculated as the difference between the maximum and minimum values in the dataset. Use the formula: $\mathrm{Range}=\mathrm{Max}-\mathrm{Min}$.
2. Step 2: Apply the range rule of thumb to estimate the standard deviation. The rule states that the standard deviation can be approximated as one-fourth of the range. Use the formula: $\sigma \approx \frac{1}{4}\times \mathrm{Range}$.
3. Step 3: Compare the estimated standard deviation to the actual standard deviation. To do this, compute the actual standard deviation using all the data points. The formula for the standard deviation is: $\sigma =\sqrt{\frac{\sum (x-\mu {)}^2}{n}}$, where $x$ represents each data point, $\mu$ is the mean, and $n$ is the number of data points.
4. Step 4: Analyze the difference between the estimated standard deviation (using the range rule of thumb) and the actual standard deviation (calculated using the formula). This comparison helps assess the accuracy of the range rule of thumb.
5. Step 5: Conclude whether the range rule of thumb provides a reasonable estimate for the standard deviation in this specific dataset. Discuss any potential limitations or factors that might affect the accuracy of the estimate.

Key Concepts

Range Rule of Thumb

The Range Rule of Thumb is a simple method for estimating the standard deviation of a dataset. It states that the standard deviation can be approximated by dividing the range of the data (the difference between the maximum and minimum values) by four. This rule provides a quick way to gauge variability without performing complex calculations, making it useful for initial assessments.

Standard Deviation

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. It is a crucial concept in statistics as it helps to understand the distribution of data points.

Data Set Comparison

Comparing estimates derived from the Range Rule of Thumb with the actual standard deviation calculated from the entire dataset allows for an assessment of the accuracy of the estimation method. This comparison can highlight the effectiveness of the Range Rule of Thumb in providing a quick approximation and can also reveal any significant discrepancies that may arise due to the nature of the data.