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Difficulty: MediumData Types, Distributions, and Descriptive Statistics

An endocrinology department evaluates the distribution of serum thyroid-stimulating hormone (TSH) levels in a population of 3,000 asymptomatic adults. In this study, the vast majority of individuals have TSH values concentrated between 1.0 and 2.0 mIU/L. However, a small proportion of the subjects have undiagnosed subclinical hypothyroidism, yielding a long tail of TSH values ranging from 5.0 to 12.0 mIU/L. Values below 0.4 mIU/L are exceedingly rare in this cohort. Based on the shape of this distribution, which of the following is the most accurate statement regarding the descriptive statistics of the TSH data in this cohort?

  1. The mean TSH value is greater than the median TSH value, and the median is the most appropriate measure of central tendency.Answer
  2. B
    The mean TSH value is greater than the median TSH value, and the mean is the most appropriate measure of central tendency.
  3. C
    The mean TSH value is less than the median TSH value, and the median is the most appropriate measure of central tendency.
  4. D
    The mean TSH value is less than the median TSH value, and the mean is the most appropriate measure of central tendency.
  5. E
    The mean and median TSH values are approximately equal, and the standard deviation is the most appropriate measure of dispersion.

Answer

The mean TSH value is greater than the median TSH value, and the median is the most appropriate measure of central tendency.
The clinical scenario describes a positively skewed (right-skewed) distribution. The bulk of the data is concentrated at the lower end, while a small number of extreme high values create a long rightward tail. In a right-skewed distribution, the mean is pulled in the direction of the long tail and thus becomes mathematically greater than the median. Because the mean is sensitive to these extreme values, the median provides a much more accurate representation of the 'typical' patient in highly skewed data and is the preferred measure of central tendency.

Step-by-Step Solution

1
Identify the shape of the data distribution based on the provided numerical ranges.
The majority of values are relatively low (1.0-2.0 mIU/L), with a long tail extending to extreme high values (5.0-12.0 mIU/L). This indicates a positively skewed (right-skewed) distribution.
Determining the direction of the skewness is necessary to understand the mathematical relationship between the mean and median.
2
Determine the effect of a positive (right) skew on measures of central tendency.
The extreme high values disproportionately pull the mean to the right, causing the mean to be greater than the median.
The mean is highly sensitive to outliers, whereas the median remains robust and resistant to extreme values.
3
Select the most appropriate statistical measure to report central tendency for skewed data.
The median is the preferred measure of central tendency.
The median accurately reflects the center of the majority of the data (the typical patient) without being distorted by the extreme outliers in the tail.

Key Concept

In a positively skewed distribution, the mean is greater than the median; the median is the preferred measure of central tendency because it is resistant to extreme outliers.
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Topics

Data Types, Distributions, and Descriptive Statistics

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