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Difficulty: MediumData Types, Distributions, and Descriptive Statistics

An oncologist is evaluating the overall survival time (in months) of patients diagnosed with advanced pancreatic adenocarcinoma who received a novel targeted therapy. The dataset includes 450450 patients. Analysis reveals that the vast majority of patients succumb to the disease between 44 and 88 months after initiating therapy. However, a small subset of patients demonstrates an exceptionally robust response, surviving for 2424 to 3636 months. Based on this distribution of survival times, which of the following statements best describes the relationship between the measures of central tendency, and which measure is most appropriate for summarizing the typical patient's survival time?

  1. The mean is greater than the median, and the median is the preferred summary measure.Answer
  2. B
    The mean is greater than the median, and the mean is the preferred summary measure.
  3. C
    The median is greater than the mean, and the median is the preferred summary measure.
  4. D
    The median is greater than the mean, and the mean is the preferred summary measure.
  5. E
    The mean and median are approximately equal, and the mean is the preferred summary measure.

Answer

The mean is greater than the median, and the median is the preferred summary measure.
The correct answer accurately describes the statistical properties of a positively skewed distribution. Because a small subset of patients survives much longer (2424 to 3636 months) than the majority (44 to 88 months), the distribution has a long right tail. These extreme high values mathematically pull the mean to the right, making it larger than the median. In any significantly skewed distribution, the median is the preferred measure of central tendency because it accurately reflects the 50th percentile and is not artificially inflated or deflated by extreme outliers.

Step-by-Step Solution

1
Determine the shape of the data distribution based on the clinical description.
The vast majority of values cluster on the lower end (44 to 88 months), with a long tail of extreme high values (2424 to 3636 months). This forms a positively skewed, or right-skewed, distribution.
Identifying the skew is necessary to understand how the mean, median, and mode relate to one another.
2
Analyze the effect of the positive skew on the measures of central tendency.
In a positively skewed distribution, the extreme high values pull the mean further to the right than the median. Therefore, the mean is greater than the median (Mean > Median > Mode).
The mean is calculated by summing all values, making it highly sensitive to extreme outliers, whereas the median relies only on the middle position.
3
Select the most clinically appropriate summary measure for skewed data.
The median is the preferred measure of central tendency.
Because the mean is distorted by the few patients with exceptionally long survival, the median provides a much more accurate representation of what the typical patient will experience.

Key Concept

In right-skewed distributions, the mean is greater than the median, and the median is the most appropriate measure of central tendency because it resists the pull of extreme outliers.
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Topics

Data Types, Distributions, and Descriptive Statistics

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