**Overview**

The normal distribution which is also known as Gaussian distribution, is a continuous distribution. This distribution looks like a bell that is why the distribution is also known as bell shaped curve.

This is considered as the most important distribution in statistics.

The data like heights, size of products produced by machines, marks of students follows normal distribution.

The data following normal distribution(Gaussian distribution) is called normally distributed data.

In this blog you will learn how to use the normal distribution.

**Parameters**

The normal distribution has two parameters, one is mean and other is standard deviation.

Mean shows where the peak of the distribution is, and standard deviation is the measurement of variability. SD defines how much the distribution is spread. If we have a smaller SD then we can conclude that the data is clustered nearly about mean and If we have a larger SD then we can conclude that the data is spread out about mean.

**Note-**

- The curve of normal distribution is symmetric about the centre.
- The total area under the curve will always be 1.
- The mean, median and mode are equal.
- Half population is greater than mean and half is less than mean
- 60% of the data lies within one standard deviation of the mean, 95% of the data lies within two standard deviation of the mean and 99.7% of the data lies within three standard deviation of the mean
- Normal distribution can be used as an approximation to the other distributions like Binomial distribution, Poisson distribution.

**Definition**

The normal distribution is given by the equation-

……..(1)

Where, is known as mean and is standard deviation.

If we put in equation (1), we get-

Here mean = 0 and standard deviation is 1.

This is called the standard form of normal distribution.

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