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The normal distribution is the most important probability distribution for understanding statistics. It is a symmetrical distribution that is often employed to represent the distribution of weights, heights, grades, etc. However, can a distribution be called normal as long as it is symmetrical?
Let’s analyze what a normal distribution is with a concrete example. Table 1 shows the statistical test scores, average values, and standard deviations of 40 first-year nursing students.
[Table 1]
In order to examine how the scores of these 40 people are distributed, we created a frequency distribution table (Table 2) with a class width of 10 points.
[Table 2]
Note that the frequency distribution graph in the figure reaches its maximum near the average value and gradually decreases as you move away from the average value. The shape of the graph is a symmetrical bell-shaped distribution.
[Figure]
A symmetrical bell-shaped curve is a normal distribution. The normal distribution is used as a model to easily represent complex phenomena in various fields of statistics and natural and social sciences.
However, even if the shape of the frequency distribution graph is a bell-shaped distribution, if the shape is too steep or too gentle, it cannot be stated that it is a normal distribution.
Statistical analysis must be conducted to determine whether the shape of the frequency distribution corresponds to the normal distribution. The main methods used to determine whether a distribution is normal are as follows:
(1) Judgment based on skewness and kurtosis
(2) Judgment based on a normal probability plot
(3) Test of normality
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