6 Real-Life Examples of the Normal Distribution


The normal distribution is the most commonly-used probability distribution in all of statistics.

It has the following properties:

  • Bell shaped
  • Symmetrical
  • Unimodal – it has one “peak”
  • Mean and median are equal; both are located at the center of the distribution
  • About 68% of data falls within one standard deviation of the mean
  • About 95% of data falls within two standard deviations of the mean
  • About 99.7% of data falls within three standard deviations of the mean

This tutorial shares 6 examples of real-world phenomena that actually follow the normal distribution.

Example 1: Birthweight of Babies

It’s well-documented that the birthweight of newborn babies is normally distributed with a mean of about 7.5 pounds.

The histogram of the birthweight of newborn babies in the U.S. displays a bell-shape that is typically of the normal distribution:

Example of normal distribution

Example 2: Height of Males

The distribution of the height of males in the U.S. is roughly normally distributed with a mean of 70 inches and a standard deviation of 3 inches.

A histogram of the height of all U.S. male reveals a bell shape:

Real-world example of normal distribution

Example 3: Shoe Sizes

The distribution of shoe sizes for males in the U.S. is roughly normally distributed with a mean of size 10 and a standard deviation of 1.

A histogram of the shoe sizes of all U.S. male reveals a bell shape with a single peak at size 10:

Example of normal distribution

Example 4: ACT Scores

The distribution of ACT scores for high school students in the U.S. is normally distributed with a mean of 21 and a standard deviation of about 5.

A histogram of the ACT scores for all U.S. high school students illustrates this normal distribution:

Normal distribution ACT scores example in statistics

Example 5: Average NFL Player Retirement Age

The distribution of retirement age for NFL players is normally distributed with a mean of 33 years old and a standard deviation of about 2 years.

A histogram of this distribution exhibits a classical bell shape:

Normal distribution real-world example

Example 6: Blood Pressure

The distribution of diastolic blood pressure for men is normally distributed with a mean of about 80 and a standard deviation of 20.

A histogram of the distribution of blood pressures for all mean displays a normal distribution with a bell shape:

Normal distribution example

Additional Resources

5 Real-Life Examples of the Poisson Distribution
5 Real-Life Examples of the Binomial Distribution
4 Examples of Using Linear Regression in Real Life
4 Examples of Using ANOVA in Real Life
4 Examples of Using Logistic Regression in Real Life

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