# Understand What the Formula of Standard Deviation is and How to Calculate Standard Deviation

## Introduction

In this article, you will understand the meaning of standard deviation and learn how to calculate it using formula.

## What is Standard Deviation?

It is a statistical term that measures the variation and dispersion of sample data. It estimates how much the values are away or close to the mean of the sample data. It is denoted by SD or a Greek letter.

In statistics, the standard deviation is an important concept. If the SD value is low, the sample values lie near the mean. If greater, the sample values will be dispersed away from the mean.

## Standard Deviation Formula

It is the measure of dispersion and variation of a data point from the mean of sample data. The formula for standard deviation is:

## How to calculate standard deviation?

It is easy to calculate standard deviation for any set of data by using its formula. If there are xi data points having the mean x, the standard deviation can be calculated as:

$$σ \;=\; SD \;=\; \sqrt{\frac{\sum_{i=1}^N (x_i - \bar x)^2}{n}}$$

Here we provide you an easy and step-by-step way of computing standard deviation.

• Find the mean of the sample data.
• Find the sum of differences of the data points with mean.
• Use the standard deviation formula by substituting required values.

## Related Formulas

### Standard Deviation Population Formula

The formula of SD for population mean is,

$$σ \;=\; \sqrt{\frac{\sum_{i=1}^n (x - μ)^2}{N}}$$

### Variance Formula

It is the square of standard deviation such that,

$$σ^2 \;=\; \frac{\sum_{i=1}^n (x - μ)^2}{N}$$

## What is the formula for standard deviation?

The formula for standard deviation is:

$$σ \;=\; SD \;=\; \sqrt{\frac{\sum_{i=1}^N (x_i - \bar x)^2}{n}}$$

Where,
xi = Value of each data point.
x = Mean
n = Number of data points.

## How do you Tell if a Standard Deviation is High or Low?

When you calculate standard deviation, it tells you the variation of data points from the mean. If it is low, it means that the data points are near to the mean. If the value of standard deviation is high, it means the data points are away from the mean.

## Why is Standard Deviation Important?

It is important because it helps to find the variation of data with respect to the mean. For example, it can help you to check the profit and loss of goods with respect to the average values.

### Shaun Murphy

Last updated: July 07, 2023

I'm graduated in biomedical and electrical engineering. Specialization in sports and medical topics but will gladly tackle everything you throw at him. He is a sailor, hiker, and motorcyclist in his free time.