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Difficulty: HardData Types, Distributions, and Descriptive Statistics

A regional health network evaluates the quality of its emergency cardiovascular care by analyzing the door-to-balloon times for 1,2001,200 patients presenting with ST-segment elevation myocardial infarction over the past year. The times are recorded as a continuous variable in minutes. A preliminary review of the data reveals a mode of 6868 minutes and a median of 8484 minutes. The distribution includes a long tail representing a small subset of patients transferred from remote rural facilities who experienced times exceeding 350350 minutes. The research committee is preparing a summary report for the hospital board. Based on the characteristics of this dataset, which of the following statements is most accurate regarding the statistical analysis?

  1. The mean door-to-balloon time is expected to be greater than 8484 minutes, and the interquartile range should be used to report data dispersion.Answer
  2. B
    The mean door-to-balloon time is expected to be less than 8484 minutes, and the standard deviation should be used to report data dispersion.
  3. C
    The data exhibits negative skewness, meaning parametric tests are preferred for inferential analysis.
  4. D
    The mean and standard deviation are the most appropriate descriptive statistics to summarize this dataset.
  5. E
    The extreme transport delays should be interpreted as isolated abnormalities and excluded from the dataset to allow the use of the standard deviation.

Answer

The statement indicating that the mean is expected to be greater than 8484 minutes and the interquartile range should be used is the most accurate.
The clinical dataset describes a right-skewed (positively skewed) distribution, as evidenced by a long tail of high values (transport delays) and the fact that the median (8484) is greater than the mode (6868). In a right-skewed distribution, the mean is disproportionately affected by the extreme high values in the tail and will be pulled to the right, making it greater than the median. When data is skewed, the mean and standard deviation are misleading representations of the 'average' patient. Instead, the median should be used to report central tendency, and the interquartile range (IQR) should be used to report dispersion, as both are robust against extreme outliers.

Step-by-Step Solution

1
Determine the shape of the data distribution.
The distribution has a mode of 6868, a median of 8484, and a long tail of high values (>350>350). Because the tail points toward higher numbers, it is a positively (right) skewed distribution.
Identifying the skew direction is required to understand the relationship between central tendency measures.
2
Analyze the effect of the skew on the mean.
In a right-skewed distribution, extreme high values pull the mean disproportionately to the right. Therefore, the relationship is Mean > Median > Mode. The mean must be greater than the median (8484 minutes).
The mean is sensitive to outliers, whereas the median is not.
3
Select the appropriate descriptive statistics for this data type and shape.
Because the continuous data is heavily skewed, parametric summary statistics (mean and standard deviation) will be misleading. Non-parametric descriptive statistics (median for central tendency, interquartile range for dispersion) should be used.
The median and interquartile range (IQR) provide a more accurate representation of the 'typical' observation and the spread of the middle 50% of the data when extreme outliers are present.

Key Concept

In positively (right) skewed distributions, the mean is greater than the median. For highly skewed clinical data, the median and interquartile range (IQR) are the preferred measures of central tendency and dispersion, respectively.
Estimated Time:1m 30s
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Topics

Data Types, Distributions, and Descriptive Statistics

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