Why is Standard Deviation important?

Hint: To discuss the importance of standard deviation, first, we need to know what is standard deviation. Standard Deviation is defined as the measure of the dispersion of data from the mean value. Dispersion over here means the deviation or the measure by which an object differs from another object. The deviation, in this case, is known as the arithmetic mean. It is always a positive value. The value of standard deviation is calculated by the square root of the mean of the square of the deviation of all the data points from the arithmetic mean.

Complete step-by-step answer:
Standard Deviation in statistics is considered important because it gives an estimation of how instances in a dataset are dispersed from the mean value. It is also known by the name, root meaning square deviation. The Standard Deviation is represented by the Greek Letter sigma \[\sigma \].
$\sigma = \sqrt {\dfrac{{\sum\limits_{i = 1}^n {{{({x_i} - \overline x )}^2}} }}{n}} $The formula for standard deviation is as follows:

where ${x_i} = $ data points in the data set
$\overline x = $mean of the dataset
The higher is the deviation or dispersion of data, the larger is the magnitude of the standard deviation value whereas the lower is the variability of data, the lower is the magnitude of the standard deviation value. The Standard deviation has a wide range of use in various fields. The main advantage of standard deviation is that it gives a more realistic picture of how the data is distributed. It is used in statistics to get the range of the distribution. Standard deviation is even used for weather forecasting. It is often used by teachers to calculate the result or range of distribution for a particular exam.

Note: It is important to note that the standard deviation value can never be negative. However, the standard deviation is $0$,if all the data points in the data set are the same. This is because if all the instances are the same then there will be no deviation from the mean. The mean in such cases will be the data point itself.