Normal distribution: what means in numbers?

Any process in which there are only random causes of variation follows a law of normal distribution. This condition that appears frequently in natural phenomena (hence it is called “normal”). When we evaluate what happens with a variable measured in a very large population, we find that these values form a bell shape.

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The largest number of individuals would be grouped around the central value, which is in turn, the mean value, and the modal value. The standard deviation (σ) is the most typical measure of dispersion, which tells us how scattered the data are in relation to the mean. While standard deviation is a typical distance from the mean, it is expected that we expect some values to be further from the mean than it.

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The proportion of measurements between mean and the deviations is a constant where:

• Mean ± 1 * standard deviation = covers 68.26% of the cases
• Mean ± 2 * standard deviation = covers 95.44% of the cases
• Mean ± 3 * standard deviation = covers 99.73% of the cases

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An example

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A city has 500,000 adults. Usually, their heights are distributed with an average of 175 cm and a standard deviation of 10 cm. So how many people would you expect to be taller than 205 cm?

The answer is mean + 3 deviations; therefore, 175 + 3 (10) = 205. Looking at the graph, the mean plus three standard deviations leave us at 0.13%

The calculation is 500,000 * 0.13% = 650. So, only 650 people in the general population will be 205 cm taller.