Normally Distributed
Analysis Of Statistical Data

Normally Distributed
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Normally Distributed

This most common distribution is your first step to the understanding of statistics.

The normally distributed statistical process, also known as the Gaussian process exhibits normal or the Gaussian distribution - one of the basic continuous probability distributions. Most real world stochastic phenomena (whose mean and variance can be computed) exhibit a behavior that can be characterized by a normally distributed variable.

Probability Density Function:

The probability density function of a normally distributed process is known as the Gaussian function, which appears in a characteristic bell shaped curve when plotted against the values of the variable.


Normal Equation

Where is the mean and 2 is the variance of the distribution.

The variance describes the spread of the distribution about the mean value. A larger 2 means greater scattering in the values taken by the variable. Resultantly, the probability of the variable to take the mean value is lower if the distribution has a smaller 2, which means that the variable is closely clustered around the mean value.

Characteristic Function Curve of the
Normally Distributed Process:

A graph of the probability density function (PDF) for normally distributed stochastic process with different values of standard deviation (square root of variance) is given below. As the variance or standard deviation increases, the height of the characteristic bell shaped curve (the probability of the variable to cluster closely around the mean value) decreases. A normal distribution also exhibits a normally distributed histogram, provided sample size is very large.

Normal Distribution Curves

Properties of a
Normally Distributed Statistical Process:

How to conduct the Process?

  1. First of all, record data for the total weight of 8 random persons:

  2. Then calculate mean value

  3. Calculate variance.

  4. Calculate standard deviation.

  5. Determine probability density function.

  6. Plot f(x) versus x over range of observations (452 ~ 692)

Other Important Statistical Distributions:

Some other fundamental statistical probability distributions are:


Normally distributed statistical processes display one of the fundamental statistical probability distributions i.e. the normal distribution. The distribution can be completely described with just two parameters: the mean, and the variance. The graph of probability density function of normal distribution is a characteristic bell curve, which is symmetric about the mean. Other important probability distributions include uniform distribution, lognormal distribution, t distribution and gamma distribution.

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Do You Want To Understand Statistics Better?

The links below are specific questions and answers about statistics and how to use them.

Standard Deviation Formula

Regression Procedure

Regression Modeling

What is the Standard Deviation?

Mean and Standard Deviation

What Is the Value of Standard Deviation in Business?

Standard Error

Analysis of the Data