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Difficulty: MediumData Types, Distributions, and Descriptive Statistics

A maternal-fetal medicine research group is analyzing gestational age at delivery (in weeks) for all live births at a regional perinatal center over a five-year period. The dataset includes 12,50012,500 deliveries. The data show that the vast majority of deliveries occur at term, between 3838 and 4141 weeks of gestation. However, there is a long tail of premature deliveries extending down to 2323 weeks of gestation, with progressively decreasing frequency at earlier gestational ages. Which of the following correctly identifies the expected shape of this data distribution, the relationship between its mean and median, and the most appropriate measure of statistical dispersion to report?

  1. Negatively skewed distribution; mean is less than median; interquartile rangeAnswer
  2. B
    Negatively skewed distribution; mean is greater than median; standard deviation
  3. C
    Positively skewed distribution; mean is greater than median; interquartile range
  4. D
    Positively skewed distribution; mean is less than median; standard deviation
  5. E
    Normal distribution; mean is equal to median; standard deviation

Answer

Negatively skewed distribution; mean is less than median; interquartile range
The data has a long tail of smaller values (premature births down to 2323 weeks) with the bulk of the data clustered at higher values (term births at 3838-4141 weeks). This asymmetric tail extending to the left defines a negatively skewed (left-skewed) distribution. In negatively skewed distributions, the extreme lower values disproportionately pull the mean to the left, making the mean less than the median. Because the data is not normally distributed, non-parametric summary measures are preferred; the interquartile range (IQR) is the most robust measure of dispersion because it is unaffected by extreme outliers in the tail.

Step-by-Step Solution

1
Identify the distribution shape from the description of the data spread.
The distribution has a peak at 38-41 weeks and a long tail extending leftwards down to 23 weeks, making it a negatively skewed (left-skewed) distribution.
Understanding the distribution shape is the first step in selecting appropriate descriptive statistics.
2
Evaluate how the negative skew affects the measures of central tendency.
The extreme low values in the left tail disproportionately pull the mathematical average down, causing the mean to be less than the median.
To determine the correct relationship between the mean and median for this specific distribution.
3
Determine the most robust measure of dispersion for skewed data.
The interquartile range (IQR) should be used because it measures the middle 50% of the data and is resistant to the extreme low values in the tail.
Standard deviation is inappropriate because it is highly sensitive to outliers and is intended for normally distributed data.

Key Concept

Effect of distribution skew on measures of central tendency and dispersion
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Topics

Data Types, Distributions, and Descriptive Statistics

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