Estimating s The sample of 92 roller coaster maximum speeds includes values ranging from a low of 10 km/h to a high of 194 km/h. Use the range rule of thumb to estimate the standard deviation.

Verified step by step guidance

1. Identify the range of the data by subtracting the minimum value from the maximum value. In this case, the range is calculated as: $R=x_{\max }-x_{\min }=194-10$.
2. Recall the range rule of thumb, which states that the standard deviation can be approximated as one-fourth of the range. The formula is: $s=\frac{R}{4}$.
3. Substitute the calculated range into the formula for the standard deviation. This gives: $s=\frac{184}{4}$.
4. Simplify the fraction to estimate the standard deviation. Perform the division: $s=184÷4$.
5. Interpret the result as the estimated standard deviation of the sample of roller coaster maximum speeds, based on the range rule of thumb.

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 complex calculations.

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 crucial for understanding the distribution of data points in a sample.

Sample Size

Sample size refers to the number of observations or data points collected in a study. In this case, the sample size is 92 roller coaster maximum speeds. A larger sample size generally leads to more reliable estimates of population parameters, such as the standard deviation, as it reduces the impact of outliers and variability in the data.