How to Calculate Standard Deviation

The Standard Deviation stands for the average amount. Further, it signifies the variability of the data set. In addition, it has 2 types of Deviations. Those are the ‘Standard & Sample’. It has a notation of the ‘σ’ symbol. Moreover, it is the Greek symbol with the name ‘Sigma’. There are different ways available for its calculation. But, many uses don’t have any idea about ‘How to Calculate Standard Deviation?’. It has various application segments, so you need to get information related to it. We are here for you with the knowledgeful data. We have also covered the article on ‘How to Calculate the Percentage‘. So, you can make use of it. Thus, let’s take a look at ‘How to Calculate Standard Deviation?’.

How to Calculate Standard Deviation?

Standard Deviation term has a very wide use. Moreover, it is a very complex process to calculate it by hand. So, it needs to follow some useful information. We are delivering here a tutorial on ‘How to Calculate Standard Deviation?’. We make sure that this elaborative data will give you satisfactory results. On the other end, get ready to grab this knowledge. Thus, don’t miss this opportunity. Let’s move towards this amazing journey now.

Methods Used For This Purpose

There are different methods available for this purpose. So, we are giving here some of them for you.

Method – 1 ) For Standard Deviation

There is specific process available for this purpose. Thus, follow the data given below to do so.

Formula:

method 1 How to Calculate Standard Deviation step 1

Here,

σ = Deviation

N = No. of entities available

xi = Individual Values,

μ = Mean of all the values.

Example:

Let’s have the values as 1, 3, 4, 7, 8.

Step – 1 ) Mean Calculation

First of all, calculate the mean for the values provided. Thus, do the necessary mathematical operation by using the formula below.

Mean (μ) = Sum of all the values / Total number of values

= (1+3+4+7+8) / 5

Mean (μ) = 4.6

Step – 2 ) Calculation For (xi – μ)

After that, moving ahead, you need to calculate the values of (xi – μ) for each value.

Here,

x1 = 1, x2 = 3, x3 = 4, x4 = 7, x5= 8.

So,

x1 – μ = 1 – 4.6 = (-3.6) & Square of (-3.6) = 12.96

x2 – μ = 3 – 4.6 = (-1.6) & Square of (-1.6) = 2.56

x3 – μ = 4 – 4.6 = (-0.6) & Square of (-0.6) = 0.36

x4 – μ = 7 – 4.6 = 2.4 & Square of 2.4 = 5.76

x5 – μ = 8 – 4.6 = 3.4 & Square of 3.4 = 11.56

Thus, the sum of the square values = 12.96 +2.56 + 0.36 + 5.76 + 11.56 = 33.2

Further,

Sum of the square values / N = 33.2 / 5 = 6.64

Step – 3 ) Calculation of Deviation

Thus, putting above values in the formula, you can easily calculate the deviation.

Deviation (σ) = √6.64 = 2577

Thus, you can use this method.


Method – 2 ) For Sample Standard Deviation

There also the definite process available for this option too. All you need to do is to follow the steps below.

Formula:

method 2 How to Calculate Standard Deviation step 1

Here,

s = Sample Standard Deviation,

N = No. of entities available,

x bar = Mean,

xi = Individual Values

Example:

Let’s have the values as 9, 2, 5, 4, 12, 7

Step – 1 ) Mean Calculation

You should calculate the mean first. So, do the operation as the given formula.

Mean (x bar) = Sum of all the values / Total number of values

= (9+2+5+4+12+7) / 6

Mean (x bar) = 6.5

Step – 2 ) Calculation For (x bar – xi)

Here,

x1 = 9, x2 = 2, x3 = 5, x4 = 4, x5= 12, x6= 7.

So,

x1 – 6.5 = 9 – 6.5 = 2.5 & the square of 2.5 = 6.25

x2 – 6.5 = 2 – 6.5 = (-4.5) & the square of (-4.5) = 20.25

x3 – 6.5 = 5 – 6.5 = (-1.5) & the square of (-1.5) = 2.25

x4 – 6.5 = 4 – 6.5 = (-2.5) & the square of (-2.5) = 6.25

x5 – 6.5 = 12 – 6.5 = 5.5 & the square of 5.5 = 30.25

x6 – 6.5 = 7 – 6.5 = 0.5 & the square of 0.5 = 0.25

Thus, the sum of the square values = 6.25 + 20.25 + 2.25 + 6.25 + 30.25 + 0.25 = 65.5

Further,

Sum of the square values / (N – 1) = 65.5 / (6-1) = 65.5 / 5 = 13.1

Step – 3 ) Deviation Calculation

Thus, put the above values in the formula. So, you can easily calculate the deviation.

s = √(13.1) = 3.619

Thus, you can use this method to complete the operation.


In this way, following the above-mentioned methods, you can fulfill the requirements.