Why is normal distribution important

Its importance will be clear from the following points: 1. The normal distribution has the remarkable property stated in the so-called central limit theorem.

Thus, if samples of large size, n, are drawn from a population that is not normally distributed, nevertheless the successive sample means will form themselves distribution that is approximately normal. As the size of the sample is increased the sample means will tend to be normally distributed. The central limit theorem applies to the distribution of most other statistics as well, such as the median and standard deviation but nor range. The central limit theorem gives the normal distribution its central place in the theory of sampling since many important problems can be solved by this single patter of sampling variability.

As a result the work on statistical inferences is made simpler. The area under the normal distribution curve represents probability and the total area under the curve sums to one. Most of the continuous data values in a normal distribution tend to cluster around the mean, and the further a value is from the mean, the less likely it is to occur. The tails are asymptotic, which means that they approach but never quite meet the horizon i.

For a perfectly normal distribution the mean, median and mode will be the same value, visually represented by the peak of the curve. The normal distribution is often called the bell curve because the graph of its probability density looks like a bell. It is also known as called Gaussian distribution, after the German mathematician Carl Gauss who first described it.

A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. Figure 1. A standard normal distribution SND. This is the distribution that is used to construct tables of the normal distribution.

The normal distribution is the most important probability distribution in statistics because many continuous data in nature and psychology displays this bell-shaped curve when compiled and graphed. For example, if we randomly sampled individuals we would expect to see a normal distribution frequency curve for many continuous variables, such as IQ, height, weight and blood pressure.

The most powerful parametric statistical tests used by psychologists require data to be normally distributed. What's So Important about the Normal Distribution? Next section: Converting to percentiles and back One reason the normal distribution is important is that many psychological and educational variables are distributed approximately normally.

Measures of reading ability, introversion, job satisfaction, and memory are among the many psychological variables approximately normally distributed.