Normal Distribution: Everything You Need to Know

This is a pattern of statistical data distribution. When graphed as a histogram, certain data forms a bell-shaped curve, which is commonly referred to as normal distribution. They are symmetrical and have a single central peak at the mean. The normal distribution is important in statistics due to several reasons. Some of these include:

·         The statistical hypothesis test assumes the data follows a normal distribution.

·         The central limit theorem establishes that as the sample size increases, the distribution of the mean follows a normal distribution regardless of the distribution of the original variable.

·         Both linear and non-linear regression assumes the residual follows a normal distribution.

A normal distribution has two main parameters: the mean and standard deviation. One can decide the probabilities and shape of the distribution concerning the problem statement with the help of these parameters.


·         Statisticians use the average or mean value as a measure of central tendency. It can be utilized to define the distribution of variables that are measured as intervals or ratios.

·         The mean establishes the location of the peak, and the majority of the data points are clustered around it in a normal distribution graph.

·         If one changes the value of the mean, the curve of normal distribution moves either to the right or left along the X-axis.

Standard deviation:

·         The standard deviation calculates how the data points are dispersed in relation to the mean.

·         It represents the distance between the data points and the mean.

·        It defines the width of the graph. Therefore, altering the value of standard deviation expands or tightens the width of the distribution along the X-axis.

·        Generally, a smaller standard deviation concerning the mean leads to a steep curve while a larger standard deviation leads to a flatter curve.

Some properties of normal distribution include:

·         The shape of the normal distribution is fully symmetrical. This means one can produce two equal halves by dividing the normal distribution curve from the middle.

·         The midpoint of normal distribution stands for the point with maximum frequency, i.e., it comprises most observations of the variable.

·       In normally distributed data, there’s a constant proportion of data points remaining under the curve between the mean and a number of standard deviations from the mean. Therefore, nearly all values lie within three standard deviations of the mean for a normal distribution. These can help one understand the appropriate percentages of the area below the curve.

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