Meaning & use
normal distribution
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Meanings
nouncountabletechnicalmathematics
A symmetric, bell-shaped probability distribution in which values cluster around the mean and become rarer farther away.
Grammar: Countable: you can say 'a normal distribution' or 'normal distributions'. Often used with 'the' when referring to the standard model.
Patterns
- a normal distribution
- follow a normal distribution
- fit a normal distribution to something
Heights in a large population often follow a normal distribution.
The data were approximately normal, so the researchers used a normal distribution.
In a normal distribution, about 68 percent of values lie within one standard deviation of the mean.
nounsingulartechnicalmathematics
The standard theoretical curve used in statistics to model random variation around an average.
Grammar: Usually with 'the' when referring to the model as a whole: 'the normal distribution'.
Patterns
- the normal distribution
- assume a normal distribution
- under the normal distribution
Many statistical tests assume the normal distribution.
The normal distribution is also called the Gaussian distribution.
Under the normal distribution, extreme values are possible but unlikely.
Word forms
| plural | normal distributions |
|---|
Common combinations
- follow a normal distribution
- Test scores in a large class often follow a normal distribution.
- approximately normal distribution
- With enough data, the sample mean has an approximately normal distribution.
- standard normal distribution
- A standard normal distribution has a mean of zero and a standard deviation of one.
- assume a normal distribution
- The analysis assumes a normal distribution of errors.
- the normal distribution curve
- The normal distribution curve is symmetric about the mean.
Synonyms and how they differ
- Gaussian distribution
- The same thing, named after the mathematician Gauss; common in physics and engineering.
- bell curve
- An informal name for the shape of the normal distribution, often used in everyday writing.
Word family
- normally distributed adjective
- Describing data that follow a normal distribution.
- normal adjective
- In statistics, relating to this distribution or to standard values.
- distribution noun
- The general mathematical term for how values are spread.
Commonly confused: normal distribution or standard distribution? normal distribution or uniform distribution?
normal distribution vs standard distribution
Not a standard term; the usual phrase is 'standard normal distribution', which is a special case with mean 0 and standard deviation 1.
normal distribution vs uniform distribution
In a uniform distribution all values are equally likely, so the shape is flat, not bell-shaped.
Practice
In a normal distribution, where do most values cluster?
Choose one answer.
The normal distribution is bell-shaped, so most values cluster around the mean. The extremes are rare, and zero is not necessarily the center.
Make it your own
Write a sentence using “normal distribution”, then check it and compare it with the examples above.