Simple Method of Calculating Standard Deviation Problems

Standard Deviation: Definition and Step-by-Step Calculation

Standard deviation refers to the means of all the averages for multiple sets of data.  It denotes a statistic that measures the dispersion of a dataset relative to its mean.  It is that statistical measurement in finance which, on application to the annual rate of return of an investment, will shed light on the historical volatility of the investment. It is a vital calculation in the field of sciences and math, especially in lab reports. Scientists and statisticians use standard deviations for determining how closely sets of data are to the mean of all the sets. The calculation is very easy to perform. There are a lot of calculations that support the calculation of standard deviation.

Once you get clarity on the use of numbers and equations, calculating standard deviation is simple. The greater the standard deviation of securities, the greater the variance between each price and mean, resulting in a larger price range. The standard deviation shows how much data is spread out around the mean and average. The standard deviation that is close to 0 indicated that the data points tend to be close to the mean.

The formula of the standard deviation:

How to Calculate Standard Deviation?

Once you go through all the steps, calculating standard deviation will not seem complicated anymore. We have used the easiest methods to help you understand how to calculate the standard deviation. You will be glad to know that most essay writer help services even prefer using this method.

  1. Find out the mean
  • Look at the data set

Taking a look at the data step is a vital step in any type of statistical calculation. Here are a few ways to do that:

  • You need to understand how many numbers are in your sample.
  • Determine if numbers vary across or are the difference between the numbers small like a few decimal places
  • Consider the type of data you are looking at. Try understanding what the numbers in your sample represent. This can be something like test scores, height, weights and heart rate reading, etc.
  • Take, for instance, a set of test scores is 10, 5, 8,6, 3, and 4
  • Gather all your data

For calculating the mean, you will require every number from the same

  • The mean will be the average of all your data points.
  • Calculate it by adding up all the numbers present in your sample and then divide the answer by the total number present in your sample.
  • So in the sample of test scores (10, 5,8,6,3 and 4) there aretotal of 6 numbers.

Hence the value of n will be 6

  • Add all the numbers present in the sample

This will be the first step of calculating a mathematical average or mean

  • 10+5+8+6+3+4= 36. 36 is the sum of all the numbers in the sample
  • Make sure you do the addition a second time for checking your answer.
  • Divide the result of addition by the total numbers present in your sample. 

By doing this, you will take out the average or mean of the data

  • There are total 6 numbers (10, 5, 8, 6, 3 and 4) in the sample or test scores. Hence, n=6
  • The total amount of the test scores is 34 So you will have to divide 36 by n to find out the mean
  • 36/6=6 
  • The main test score in the sample is  6
  1. Calculate the variance in your sample
  • Find the variance

The variance refers to the figure representing how far the data in your sample is clustered around the mean.

  • It will give you an idea regarding how far the data is spread out.
  • Samples with low variance will include data that is clustered closely around the mean
  • Samples with high variance have data clustered far from the mean
  • Variance is used for comparing the distribution of two data sets.
  • Subtract mean from each of the numbers in the sample

It will show how much each data point differs from the mean.

  • 10-6=4, 5-6=-1, 8-6=2, 6-6=0 ,3-6= -3 and 4-6= -2

Do the subtractions again to re-check each of the answers to ensure you have the correct figure.

  • Find out the square of the numbers of each subtractions

Each of these figures will be required for finding out the variance in your sample.

  • When you subtracted the mean (6) from each of the numbers (10, 5,8,6,3 and 4), the result was the following: 4, -1, 2,0, -3, and -2
  • Now for the next calculation in figuring out variance, you will perform the following: 

42, (-1)2, 22, 02, (-3)2 and (-2)2 = 16, 1, 4, 0, 9 and 4

  • Make sure you check your answer before proceeding to the next step.
  • Add the squared numbers together

This figure is known as the sum of squares.

The square result of the example was as follows: 16, 1, 4, 0, 9 and 4

  • 16+1+4+0+9+4= 34. Therefore the sum of squares is 34.
  • Divide the sum of squares by (n-1)

Remember n represent the total numbers presents in your sample. This step will provide the variance

  • N-1=5. The sum of the square for the sample was 34
  • Thus, 34/5=6.8
  • Hence, the variance in the sample is 6.8
  1. Calculating the standard deviation
  • Take the square root  of the variance

You will require finding the square root of the variance, 6.8

Thus square root of 6.8 will be 2.60768096

  • Go through the mean, variance and standard deviation once again

It is important that you go through all the steps of the calculations by hand or using a calculator.  If you come with a different answer the second time around, make sure that you check your work. If, in the third time, you are unable to find your mistake, start over re-checking again to compare your work.


Standard deviation, on, average lets you know how far each score lays from the mean. A higher standard deviation will mean that the values are far from the while; a low standard deviation means values are clustered close to the mean. You do not need to shy away if you are unaware of how to calculate the standard deviation. Just make sure you have the patience to learn it step by step.

AUTHOR BIO: Clara Smith is a maths professor in one of the reputable universities in the USA. She is also associated with where she is an eminent essay writer. She also shares a passion for playing the piano. 

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