Conditions For Using The Empirical Rule
A researcher analyzed the mileage data for New York City taxis, summarized in the table below. Applying the empirical rule, the researcher stated that 68% of taxis have a mileage between and miles. However, a subsequent examination revealed that the distribution of the mileage data is skewed. What was the researcher’s primary error in this application of the empirical rule?
Taxi Mileage Summary
| Statistic | Value |
|---|---|
| Mean () | 75000 |
| Standard Deviation () | 12000 |
| (Other details omitted) |
He multiplied the mean by the standard deviation instead of adding and subtracting.
He assumed normality and applied the empirical rule without verifying that the data distribution was approximately normal.
He used the median instead of the mean for the empirical rule calculations.
He incorrectly recalculated the boundaries by using the range rather than the standard deviation.
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