Normal distribution: what it is, characteristics and examples in statistics

In statistics and probability, the normal distribution, also called the Gaussian distribution (in honor of Carl F. Gauss), Gaussian distribution or Laplace-Gauss distribution, reflects how the data is distributed in a population.

It is the most frequent distribution in statistics, and it is considered the most important due to the large number of real variables that take its form. Thus, many of the characteristics in the population are distributed according to a normal distribution: intelligence, anthropometric data in human beings (for example height, height ...), etc.

Let's see in more detail what the normal distribution is, and several examples of it.

• Related article: "Psychology and statistics: the importance of probabilities in behavioral science"

What is the normal distribution in statistics?

The normal distribution is a concept belonging to statistics. Statistics is the science that deals with the counting, ordering and classification of the data obtained by the observations, in order to make comparisons and draw conclusions.

A distribution describes how certain characteristics (or data) are distributed in a population. The normal distribution is the most important continuous model in statistics, both due to its direct application (since many variables of interest can be described by this model), as well as by its properties, which have allowed the development of numerous inference techniques statistics.

The normal distribution is, then, a probability distribution of a continuous variable. Continuous variables are those that can take on any value within an interval that is already predetermined. Between two of the values, there can always be another intermediate value, which can be taken as a value by the continuous variable. An example of a continuous variable is weight.

Historically, the name "Normal" comes from the fact that for a time it was believed by physicians and biologists that all natural variables of interest followed this pattern.

• You may be interested: "The 11 types of variables used in research"

Characteristics

Some of the most representative characteristics of the normal distribution are the following:

1. Mean and standard deviation

To the normal distribution corresponds to a zero mean and a standard deviation of 1. The standard deviation indicates the separation that exists between any value of the sample and the mean.

2. Percentages

In a normal distribution, you can determine exactly what percentage of the values ​​will fall within any range specific. For example:

About 95% of the observations are within 2 standard deviations of the mean. 95% of the values ​​will be within 1.96 standard deviations with respect to the mean (between −1.96 and +1.96).

About 68% of the observations are within 1 standard deviation of the mean (-1 to +1), and about 99.7% of the observations would be within 3 standard deviations of the mean (-3 to +3).

Examples of Gaussian distribution

Let's take three examples to illustrate, for practical purposes, what the normal distribution is.

1. Height

Let's think about the stature of all Spanish women; said height follows a normal distribution. That is, the height of most women will be close to the average height. In this case, the average Spanish height is 163 centimeters in women.

On the other hand, a similar number of women will be a little taller and a little shorter than 163cm; only a few will be much higher or much lower.

2. Intelligence

In the case of intelligence, the normal distribution is fulfilled worldwide, for all societies and cultures. This implies that most of the population has a medium intelligence, and that at the extremes (below, people with intellectual disabilities, and above, gifted), there is less of the population (the same% below than above, approximately).

• You may be interested: "Theories of human intelligence"

3. Maxwell curve

Another example that illustrates the normal distribution is the Maxwell curve. The Maxwell curve, within the field of physics, it indicates how many gas particles are moving at a given speed.

This curve rises smoothly from low speeds, peaks in the middle, and descends smoothly toward high speeds. Thus, this distribution shows that most particles move at a velocity around the average, characteristic of the normal distribution (concentrating most of the cases in the half).

Bibliographic references:

• Quintela, A. (2005). Sweetened Basic Statistics. Bookdown.
• Fontes de Gracia, S. Garcia, C. Quintanilla, L. et al. (2010). Research fundamentals in psychology. Madrid: UNED. ISBN: 9788436260557.
• Bottle, J. Sueró, M. Ximénez, C. (2012). Data analysis in psychology I. Madrid: Pyramid. ISBN: 9788436815382.