How To Calculate Standard Deviation

Posted on by

It is very important for us to know how to calculate standard deviation. Standard deviation is basically use as measure of variability or diversity. It is the main factor that leads to create good statistical data especially in summarizing the population, creating poll surveys, and many more. In this way, when we compare statistical data to the data in the previous years, we are able to determine how much difference there is from the expected value. For instance, a low standard deviation means that the data is very close to the expected value, otherwise; it means that data points are disperse over large range of values.

The Main Process of calculation

1. Get the Mean
2. Get the deviations
3. Square the deviation
4. Add the squares
5. Divide by total numbers less one
6. Square root of result is Standard Deviation

Execution of the Method of Calculation

By following the steps below, you will be able to calculate the standard deviation.


1.    First, determine the mean by adding up all the numbers and dividing them based on how many they are. For instance, in the list of numbers 1, 3, 4, 6, 9, 19, the mean is calculated through (1+3+4+6+9+19) 6 which will lead to the answer of 42. Divide 42 by 6 again and the answer is 7.


2.    Next, subtract the mean from every number in order to get the list of deviations and create a list of them.


3.    Then, square the resulting list of numbers or deviations.


4.    After such, add up the answers to get the total sum and divide the result by one less than number of items in the list.


5.    Square the answer and then you will have the standard deviation.

Important Keys to Take Note

Calculating Standard deviation is just like calculating the variance. However, it is very important to take note that before we get the exact standard deviation; we need to get the variance first. In order not to be confused, might as well copy the formula, which is σ = √[ ∑(x-mean)2 / N ]. In this way, you would not get lost in the middle of calculation. It may be a bit confusing but when understanding standard deviation can actually be just so straightforward. To do this, simply remember the following and do a self check whether or not the solution on how to get the standard deviation is correct.


•    Solve with the formula
•    The number of deviation should be determined before the mean
•    Know the mean in order to get the respective deviation
•    List the respective deviation from the mean
•    The answer must be a square of the result when you divide the answer scores of the latter minus one

How To Get The Standard Deviation

The Steps on how to Find Standard Deviation

Posted on by

Economics majors usually endure subjects that talks about standard deviation. Well then, there must not be many questions about this. Standard deviation is actually a significant key in interpreting statistical data and the mean itself. This topics are well studied by economics majors in order to acquire reliable data which we can base significant researches, monitor economic development, as well as compare the status of the country with at present to the previous years.


However, the steps on how to find standard deviation may be challenging that most complain about it. In truth, the generosity of the geniuses and the availability of the third media have actually helped students and even ordinary people solve their dilemma or best aid their way to get accurate answers. This fact must not actually worry students anymore.

Finding Standard Deviation Manually

Most teachers usually require just a pen and paper on desk to solve a problem on the board. In this case, all you have to do is to follow the steps in calculating for the standard. For instance, in a situation where the teacher asks the process on how to find the standard deviation for 4, 9, 11, 12, 17, 5, 8, 12, 14 just remember the following steps.

•    Get the mean. Add all the numbers and divide them base on how many they are.
•    Subtract the mean from each of the number
•    Square the deviation- this the list of numbers as a result from subtraction
•    Add the squares, these are the answers to the squares
•    Divide the number less than one
•    Square root the answer and whatever shows after doing such is the standard deviation

Finding the Standard Deviation through Calculator

Another technique to find the standard deviation is through the use of calculator. Using calculator is the easiest way to calculate the standard deviation. All you have to know the signs in the calculator and follow the methods of calculations. The following are steps on how to calculate standard deviation using Casio FX 115 ES.
•    Press the mode button
•    Press 3 for stat
•    Press 1 for 1-VAR
•    Enter the data such as 11, 12, 17, 5, 8, 12, 14
•    Press SHIFT 1 for (STAT)
•    Press 5 for VAR
•    Press 3 for population standard deviation or press 4 for sample standard  deviation
•    Press 2 to get the mean

The Importance of Accuracy

In economics, the steps on how to find standard deviation must be followed strictly to arrive in an accurate and accountable result. Although, it the answer might just be an expected or estimated amount of real statistics, the most important is that the answer is accurate because you have followed the correct formula. It should be noted that getting the correct answers through reliable calculations will help interpret statistical data. For instance, finding the standard deviation among Americans entails a serious research and tough data gathering. It should also be realized that the point of standard deviation is to measure the dispersion between the given data set. Hence, in the United States wherein the height of Americans is 70 inches with a standard deviation of 3 inches would mean that almost 68 percent of the population have a height less than or more than of the mean, that is 67 inches to 73 inches.

How To Find Standard Deviation