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.
Mean:
· 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.
