Estimate the standard deviation using the range rule of thumb.
Understand the Problem
The question is asking for an estimation of the standard deviation using the range rule of thumb. This rule suggests that the standard deviation can be approximated by dividing the range (the difference between the maximum and minimum values in a dataset) by 4. The question implies a need for a simple explanation or calculation method based on this principle.
Answer
The estimated standard deviation is approximately $\frac{\text{Range}}{4}$.
Answer for screen readers
The estimated standard deviation is given by the formula: $$ \text{Standard Deviation} \approx \frac{\text{Range}}{4} $$
Steps to Solve
- Identify the Maximum and Minimum Values
Look at the dataset and find the maximum (highest) and minimum (lowest) values.
- Calculate the Range
Subtract the minimum value from the maximum value to find the range: $$ \text{Range} = \text{Maximum} - \text{Minimum} $$
- Apply the Range Rule of Thumb
Use the range to estimate the standard deviation. According to the range rule of thumb, the standard deviation is approximately: $$ \text{Standard Deviation} \approx \frac{\text{Range}}{4} $$
- Finalize the Calculation
Plug the value of the range into the formula from the previous step to compute the estimated standard deviation.
The estimated standard deviation is given by the formula: $$ \text{Standard Deviation} \approx \frac{\text{Range}}{4} $$
More Information
The range rule of thumb provides a quick way to estimate standard deviation without complex calculations. It is useful for understanding variability in data sets, especially when full details aren't available.
Tips
- Forgetting to correctly identify the maximum and minimum values, which can lead to an incorrect range.
- Misapplying the formula by not dividing by 4 after calculating the range.
