Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
3. Describing Data Numerically
Standard Deviation
Problem 3.q.9
Textbook Question
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.

1
Identify the range of the data by subtracting the minimum value from the maximum value. In this case, the range is calculated as: .
Recall the range rule of thumb, which states that the standard deviation can be approximated as one-fourth of the range. The formula is: .
Substitute the calculated range into the formula for the standard deviation. This gives: .
Simplify the fraction to estimate the standard deviation. Perform the division: .
Interpret the result as the estimated standard deviation of the sample of roller coaster maximum speeds, based on the range rule of thumb.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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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.
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