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.

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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

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}

Substitute the calculated range into the formula for the standard deviation. This gives:

s = \frac{184}{4}

Simplify the fraction to estimate the standard deviation. Perform the division:

s = 184 \div 4

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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주요 개념

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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.