According to the range rule of thumb, the standard deviation of a data set can be roughly estimated as $\frac{\mathrm{Range}}{4}$.

• A. $\frac{\mathrm{Range}}{10}$
• B. $\frac{\mathrm{Range}}{2}$
• C. $\frac{\mathrm{Range}}{4}$
• D. $\frac{\mathrm{Range}}{6}$

Answer: (C)

Verified step by step guidance

1. Understand that the range rule of thumb is a simple method to estimate the standard deviation of a data set using the range, which is the difference between the maximum and minimum values.
2. Recall the formula for the range rule of thumb: the standard deviation \( \sigma \) is approximately equal to the range divided by a constant.
3. Identify the constant used in the range rule of thumb, which is typically 4, based on empirical observations for many data sets.
4. Write the formula as: \[ \sigma \approx \frac{\text{Range}}{4} \]
5. Use this formula to estimate the standard deviation when you know the range of the data set.