Normal Distribution

Carl Friedrich Gauss, a celebrated mathematician invented a model for the distribution of a set of data. This distribution takes the shape of a bell-shaped curve and is known as normal distribution or Gaussian distribution. Normal distribution is an essential component in the field of statistics. Sampling distribution of sample mean is a good example of normal distribution.

Normal distribution curve is always bell shape in nature. This bell shape curve comprises of several properties that include the following:

• This curve is generally intense in the central part and diminishes on either sides. This implies that there is a minimal tendency of the data to produce unusual extreme values as compared to other distributions used in statistics.

• The bell shape is always symmetric, which implies that the probability of deviations from the mean value can be compared in either direction.

Thus, normal distribution is represented in a graph form showing the bell shape curve.

Normal distribution in a variate X that has a mean µ and variance σ² can be defined as a statistical distribution that has a probability distribution P(x). The domain of X lies between –œ to +œ.

Standard Normal Distribution

A normal distribution with a mean value of 0 and a standard deviation of 1 is known as standard normal distribution. Any given normal distribution can be transformed into standard normal distribution by using the formula:

Z= (X – µ)/σ

Where X is the variate, whose normal distribution is represented, µ is the mean of the original normal distribution and σ is the standard deviation. Z is used here to represent the standard normal distribution.

There are several psychological factors that are used in economics. These psychological factors are used as variables when employed in statistical calculations. These psychological factors are mostly normally distributed. In order to transform the qualitative factors into quantitative factors, normal distribution is necessary. Normal distribution can be calculated easily and it is an easy method for mathematical statisticians.

In an economics context, a normal distribution is used to describe the distribution of data such as:

• Wealth
• Consumer sentiment
• Income
• Prices
• Supply
• Demand

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