Normal Distributions in Medical Statistics

The normal distribution depends on two parameters – bias and scale, that is, from the mathematical point of view, not on one distribution but their whole family characterized by non-typical features. The values of such parameters correspond to the mean (mathematical expectation) and spread (standard deviation) values. Standard normal distribution is a normal distribution with a mathematical expectation of 0 and a standard deviation of 1 (Jamali, Arj, Razavizade, & Aarabi, 2016).

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A normal distribution is a symmetrical distribution of a bell-shaped shape, in which about 68% of the data differs from the arithmetic mean by not more than one, and about 95% is no more than two standard deviations in each direction (Jamali et al., 2016, p. e2630). These indicators are responsible for applying statistical calculations to determine certain parameters and correlations.

In most cases, the distribution of data from biomedical research is asymmetric. It should also be noted that a normal distribution can take place only for continuous quantitative variables. If the trait in question is a qualitative, ordinal, or even quantitative discrete, its distribution cannot be normal. For instance, the number of family members, the number of antibiotics prescribed, the number of changes in antibacterial therapy, the number of rooms in the room, and other examples. Statistical processing of such characteristics should be performed by using nonparametric methods.

When taking such variables as height and weight, the latter will probably have a larger standard deviation. Growth is the value that, as a rule, does not depend on a person, and the weight of many people is dynamic. In case of any shift in the mode of life, the body mass parameter may vary by the influence of external circumstances, and its values may vary to a greater or lesser extent. Therefore, such a variable is considered dynamic with a larger standard deviation.


Jamali, R., Arj, A., Razavizade, M., & Aarabi, M. H. (2016). Prediction of nonalcoholic fatty liver disease via a novel panel of serum adipokines. Medicine, 95(5), e2630. Web.

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