How To Calculate Standard Deviation?

Standard Deviation is a measurement factor used explicitly for statistical calculations and experiments. The Standard Deviation (SD) is represented by Greek letter sigma σ or the Latin letter “s.” The SD is used to quantify the amount of variation or dispersion of a set of data values. If the Standard Deviation is low, it refers that the data tends to be close to the mean which is also known as the expected value of the set. While on the other hand, the high cost of Standard Deviation indicates that the data points have a wide range of values. As now we know how the Standard Deviation helps in calculations, let’s dig into the methods of how to find the Standard Deviation of a Set.

In the first step, we will be finding the mean, or you can say the expected value of the set. First, you need to check out your sample set. Check how many numbers are there, how much do they vary, what do they represent. To calculate the mean of the given data set, you’ll be needing all the numbers present in the dataset because the way is defined as the average value of all the data points. To find the way, you have to collect all the numbers from the dataset and them. Then you have to divide the answer by how many no are there in the set.

For better understanding, Let’s say we have a set of data of test scores(n). They are 10, 8, 10, 8, 8, 4. So, there are six numbers of data in the set n. Going ahead, first add these numbers together. The result will be 48. In the next step, divide the result with no of data present in the set. In our case, we have six numbers in our collection of data. After dividing the result with the number, we have 8. Therefore, we got the mean for our set which is 8.

Moving on to the next step, you have to find the variance in the sample. Talking of variance, it is a figure that represents the distance in which the data from the sample are situated around the mean. It will let you know about how far your data is spread out. Those who have low variance are close to the mean, while the data with high variation are now from the mean. To find the variation of your data, subtract the mean from each of your data. With the numbers in the result, take the square of each of them. After finding the square of each figure, add them together.

In our case, we have the mean which is 8. Now let’s subtract eight from each number. After subtracting, we have 2, 0, 2, 0, 0, -4. As said earlier, now take the square of each of the number. Then we have 4, 0, 4, 0, 0, 16. Following the above method, let’s add the numbers together. The result is 24.

In the final step to find the variance, we have to divide the above result with n-1. For a quick replay, n is the no of data available in the sample. In this case, we have n=6. Now following the formula we have,

24/(6-1) = 24/5 = 4.8

Therefore, the variance we got is 4.8. To find the standard deviation, the variance value plays a key role. The formula to calculate the standard deviation is to take the square root of the variance. In this case, we have the variation which is 4.8. Now after taking the square root of the variation we have 2.19. Finally, this is the Standard Deviation for the given sample.