How To Draw A Normal Curve With Mean And Standard Deviation

Introduction to Normal Distributions

David Chiliad. Lane

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Prerequisites

Distributions, Cardinal Tendency, Variability

Learning Objectives

Depict the shape of normal distributions
Country 7 features of normal distributions

The normal distribution is the near important and well-nigh widely used distribution in statistics. It is sometimes called the "bong curve," although the tonal qualities of such a bell would exist less than pleasing. It is also called the "Gaussian bend" later on the mathematician Karl Friedrich Gauss. As you lot will run across in the department on the history of the normal distribution, although Gauss played an of import role in its history, Abraham de Moivre first discovered the normal distribution.

Strictly speaking, information technology is not correct to talk nigh "the normal distribution" since there are many normal distributions. Normal distributions can differ in their means and in their standard deviations. Effigy 1 shows 3 normal distributions. The dark-green (left-virtually) distribution has a hateful of -three and a standard deviation of 0.5, the distribution in red (the middle distribution) has a mean of 0 and a standard deviation of 1, and the distribution in black (right-most) has a mean of 2 and a standard deviation of 3. These as well as all other normal distributions are symmetric with relatively more values at the center of the distribution and relatively few in the tails.

Figure ane. Normal distributions differing in hateful and standard deviation.

The density of the normal distribution (the height for a given value on the x centrality) is shown beneath. The parameters μ and σ are the mean and standard deviation, respectively, and define the normal distribution. The symbol e is the base of operations of the natural logarithm and π is the abiding pi.

Since this is a non-mathematical handling of statistics, exercise not worry if this expression confuses y'all. Nosotros will not be referring dorsum to information technology in later on sections.

7 features of normal distributions are listed below. These features are illustrated in more particular in the remaining sections of this chapter.

Normal distributions are symmetric around their mean.
The mean, median, and manner of a normal distribution are equal.
The area nether the normal curve is equal to 1.0.
Normal distributions are denser in the center and less dumbo in the tails.
Normal distributions are defined by 2 parameters, the mean (μ) and the standard deviation (σ).
68% of the expanse of a normal distribution is within one standard difference of the hateful.
Approximately 95% of the area of a normal distribution is inside two standard deviations of the hateful.

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