# How to calculate Standard Deviation problem with example & Formula:

**How to calculate Standard Deviation problem with example & Formula:**

The Standard deviation is a measure of simple spread of the data,the symbol of the standard deviation is **σ** (A Greek letter Sigma).

The formula of the standard deviation is:

** ****σ=****(xi-****)2/N**

**σ=Population of the standard deviation **

**N=Size of the population**

Xi**=Each value of he population**

**=Mean of the population**

The Standard Deviation Calculator is implementing the above formula to find the calculations easily.There are two way o9f finding the dispersion of the data, whether you are going to find the standard deviation of the whole set of the data or finding the standard deviation of the sample of the data.When you are able to extract the mean values, then you have to subtract all the values from the mean values and to take the square of the data. Then again find the square of the mean values and then find the square root of the data. This would be a manual method of finding the standard deviation. You can put the formula **σ**=(xi-)2/N to the data to find the standard deviation by the sd calculator.When you are finding the standard deviation of the whole population, it is better to utilize the population standard deviation calculator, and when finding the standard deviation of the sample then it is best to find the standard deviation of by the sample standard deviation calculator. To find the mean value from a set of the data set,it is best to utilize the mean and standard deviation calculator. To calculate standard deviation readily, it is best to use the Standard Deviation Calculator,as the online tools and the calculators are efficient to find the standard deviation of any set of the data.

## The Standard Deviation Example:

Consider the following set of data, like:

9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4

We are using the Standard Deviation Calculator, as we are finding the standard deviation manually.

To find the standard deviation,we need to follow the steps:

- Find the mean the simple average of eh numbers
- Then for the each set of he number, subtract the mean values and square the result
- Now work out the mean of those squared difference
- Take the square root of the mean values and we have done and calculate the standard deviation of the any dataset

The formula of the standard deviation actually explain all and we will explain it:

Consider we have the dataset values:

**9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4**

To find the standard deviation, we need to follow the steps given below:

## Step 1:

**Find the mean:**

### In the above formula **μ** (the greek letter “mu”) is actually the mean of all the given values of the dataset

### Consider the example:

**9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4**

The mean of that dataset values is calculated as follows:

**9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+4=140**

The total number of the dataset=20

The mean or **μ = 7**

## Step2:

Then for each of the numbers subtract the mean and square the result:

(9 – 7)2 = (2)2 = **4**

(2 – 7)2 = (-5)2 = **25**

(5 – 7)2 = (-2)2 = **4**

(4 – 7)2 = (-3)2 = **9**

(12 – 7)2 = (5)2 = **25**

(7 – 7)2 = (0)2 = **0**

(8 – 7)2 = (1)2 = **1**

We get the following result

4, 25, 4, 9, 25, 0, 1, 16, 4, 16, 0, 9, 25, 4, 9, 9, 4, 1, 4, 9

The Standard Deviation Calculator is doing all the steps in a matter of seconds and we have no need to do all the spots to find the standard deviation for any set of data.

## Step 3:

Then to find the mean of those square differences, you need to find the addition of all the values and divide by the total number of the values. In simple words, you are finding the average of the dataset. We use the symbol Σ, to find the total sum of values.

The total sum of all the values is equal to 178.

**= 4+25+4+9+25+0+1+16+4+16+0+9+25+4+9+9+4+1+4+9 = 178**

To find the mean value, we are dividing 178 by 20 which is the equal total number of the values.

Mean of squared differences = (1/20) × 178 = 8.9 and the value is also called the variance of the dataset.

## Step 4:Take the Square root of Variance:

When we are taking the square root of the variance, then we are actually able to find the standard deviation or the σ = √(8.9) = **2.983.**

**So the standards deviation of the dataset **9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4 is equal to the σ = √(8.9) = **2.983.**

The Standard Deviation Calculator is doing all the steps readily and we have no need to do all the spots.

**The final thought:**

The standard deviation is one of the basic statistical tests to find the nature and the depression of the data. The standard deviation is often described as the “Std Dev” or “SD”, it provides an induction on how far the responses of a simple question may vary or dataset, especially when doing the research. The standard deviation tells the researchers how spread out the responses to their values are. This explains how concentrated the data or the data around the mean or the scattered data is, and it expands the researchers to the extent to which the population is diversified. The Standard Deviation Calculator can be a great source in finding the result of the responses in a matter of seconds.