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Difficulty: EasyData Types, Distributions, and Descriptive Statistics

An infectious disease researcher is analyzing the incubation period of a newly identified respiratory virus. Data from 500500 confirmed cases shows that the majority of patients develop symptoms 33 to 55 days after exposure. However, a small cluster of 1515 patients did not develop symptoms until 1414 to 2121 days after exposure. The researcher needs to report a summary statistic that best represents the central tendency of the incubation period for this population without being disproportionately influenced by the unusually long incubation times. Which of the following is the most appropriate statistical measure to report?

  1. MedianAnswer
  2. B
    Arithmetic mean
  3. C
    Standard deviation
  4. D
    Variance
  5. E
    Range

Answer

Median
In this scenario, the incubation period data has a right-skewed (positively skewed) distribution, characterized by a large cluster of typical values (33 to 55 days) and a long tail of extreme higher values (1414 to 2121 days). When data is skewed, the arithmetic mean is pulled toward the tail, making it less representative of the typical value. The median is robust against extreme outliers because it simply represents the middle position of the ordered data. Therefore, it is the most appropriate measure of central tendency to report.

Step-by-Step Solution

1
Analyze the distribution shape based on the provided data.
The majority of data points are clustered at lower values (33 to 55 days), while a small number of extreme outliers exist at higher values (1414 to 2121 days). This indicates a right-skewed (positively skewed) distribution.
Understanding the shape of the data distribution is necessary to select the appropriate descriptive statistic.
2
Determine the requested metric.
The researcher needs a measure of central tendency to represent the typical incubation period without being heavily influenced by outliers.
Matching the clinical need to the correct statistical property.
3
Select the most robust measure of central tendency for skewed data.
The median is selected because it is resistant to extreme outliers.
The mean would be artificially elevated by the long incubation periods, whereas the median better reflects the typical patient experience.

Key Concept

The median is the preferred measure of central tendency for highly skewed data distributions because it is not disproportionately affected by extreme outliers.
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Topics

Data Types, Distributions, and Descriptive Statistics

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