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Biostatistics and Epidemiology for the Toxicologist: Measures of Central Tendency and Variability—Where Is the “Middle?” and What Is the “Spread?”

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Authors and Affiliations

  1. Division of Medical Toxicology, Ronald O. Perelman Department of Emergency Medicine, NYU Grossman School of Medicine, 455 First Avenue, Room 124, New York, NY, 10016, USA

    Sanjay Mohan & Mark K. Su

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  1. Sanjay Mohan
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  2. Mark K. Su
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Correspondence to Sanjay Mohan.

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Supervising Editor: Mark B. Mycyk, MD

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Key Points

• In a normal (or Gaussian) distribution, the mean, median, and mode are all the same value and the data will follow a “bell shaped” curve.

• Outliers in a sample may skew the data set and “pull the mean” away from the true “center” of the data especially when the study sample size is small. In cases like this, the median represents a better measure of central tendency.

• A large sample size reduces sampling error and thus more accurately reflects the characteristics of a population. If the sample size is large enough, its measures of central tendency appear to resemble a normal distribution even if the sample is skewed or has outliers.

• Variance and standard deviation are mathematical tools used to describe the spread of a data set and represent the homo- or heterogeneity of the data. Datasets with a small or narrow variance (or standard deviation) are more homogeneous than datasets with a large or wide variance (or standard deviation).

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Mohan, S., Su, M.K. Biostatistics and Epidemiology for the Toxicologist: Measures of Central Tendency and Variability—Where Is the “Middle?” and What Is the “Spread?”. J. Med. Toxicol. 18, 235–238 (2022). https://doi.org/10.1007/s13181-022-00901-7

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  • DOI: https://doi.org/10.1007/s13181-022-00901-7

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