Measures of Center, Spread, and Shape
Explore how measures of center spread and shape help describe data distributions using statistical concepts like mean median mode variance standard deviation skewness and kurtosis. Understand how to interpret outliers and variability in real-world data through analysis and visualization techniques.
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Emergency-department wait times for one shift are 8, 10, 11, 12, 12, 14, and 95 minutes. Most patients waited less than 15 minutes, but one 95-minute wait changes any single summary we report. If the analysis-ready DataFrame contains wait times like these, the practical question is not merely which average to calculate. We need to decide what number describes a typical wait and how variable the waits were.
A distribution is the set of observed values together with how often each value occurs. The values above concentrate near 12 minutes and stretch far to the right because of the 95-minute wait. That extreme observation is an outlier, a value far from most observations. An outlier may represent a real operational failure rather than bad data, so we should not remove it simply because it is inconvenient.
Choosing a center
Because one average can hide the usual patient experience, measures of center describe a typical location in different ways. The mean adds all wait times and divides by the number of waits. The median is the middle value after sorting. The mode is the most frequent value.
The calculations below use the same seven waits. They produce three answers to the same question, and the differences ...