In mathematics, standard deviation (abbreviated as SD) is a term that indicates the spread of a set of data around the mean or average value. It is represented by a numerical value and has the same unit as the data sets. The different values of a data set can be widely spread or can be very close to each other. So only the mean value doesn’t give an indication of how far the data is spread between the smallest and largest numbers of data set. The mean value of two different data sets can be the same but the data values of two sets can be dispersed differently. This means, with the same mean value the standard deviation can be different for different sets of data. Let’s learn about the standard deviation formula.

**For example, there can be two sets of data as follows:**

**20, 15, 22, 18, 15****3, 16, 27, 9, 35**

The means value of both the data sets is the same which is 18. However, the second set of data is clearly more spread out from the mean value than the first one. So the standard deviation of both data sets will be different. A low standard deviation indicates that data values are clustered around the mean and a high standard deviation indicates data values are more dispersed.

Standard deviation is a measure of the variation of each data point from the mean. A small standard deviation means that all the values of a set of data are close to the mean or average value, whereas a large standard deviation means that the values in the data set are farther away from the mean. This is the case where the concept of standard deviations becomes useful. In statistics, the standard deviation refers to the degree of dispersion or the spread of the data points relative to the mean and it is a measure of the variation of data values from the mean.

Standard deviation is one of the basic methods used in statistical analysis to get an idea about how the data is spread out around the average value. It gives a measure of whether most of the values in a data set are close to the mean or lots of data are far above or far below the mean value.

## Method of Finding Standard Deviation

The steps used for finding the standard deviation of a set of data are as follows:

- Find the average or arithmetic mean of the given data values.
- For each data, find its difference from the mean and take a square of that value.
- Add all the squared differences and divide the sum with the number of observations. This gives the variance.
- Find the square root of variance which gives the value of standard deviation.

In a practical scenario, the measure of standard deviation can be very useful in certain situations where the goal is to restrict the output results in a narrow span around the standard value, as in product manufacturing and quality control systems.

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