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 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:
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 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:
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:
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:
Additional Resources
The following tutorials share examples of other probability distributions in real life:
5 Real-Life Examples of the Poisson Distribution
5 Real-Life Examples of the Binomial Distribution
5 Real-Life Examples of the Geometric Distribution
5 Real-Life Examples of the Uniform Distribution
How normal distribution curve can be used in school setting?
Can you give me example how I can use normal distribution curve in school setting?
Is life expectancy a normal distribution
Could you please cite the sources for these data sets? Thank you!
I was looking for examples of normal distributions for a stats class I teach in a sociology department. Based on 2022 data from the US Census Bureau, the distribution of income inequality in census tracts takes an approximately normal shape.
Hi Jeff…Using the distribution of income inequality in census tracts as an example is a great choice for demonstrating normal distribution principles in a relatable way. You might also highlight how the shape provides insights into the spread and central tendency of income levels. Additionally, this example can spark discussions on the real-world implications of income inequality patterns in different regions, enriching students’ understanding of both statistics and sociology.
If you need any supplementary material, like visualizations or additional data points, let me know—I’d be glad to help!