As you know, a standard deviation is a quantitative measurement of the amount of dispersion of the observations in a group from its mean value. So if you want to learn standard deviation from the beginning here we have provided you standard deviation for dummies in easy steps. Standard deviation is an important concept in mathematics and statistics so it is important for students to learn standard deviation to understand the concepts in science and maths better.
Standard Deviation For Dummies With Example
Standard deviation is simply the quantitative measurement of how much the numbers in a group are sreaad out from the central mean value of the group. It is represented by the Greek alphabet σ (or sigma). A low standard deviation indicates that the data in the group are less spread out from the group, and hence are closer to the mean value of the group. A high standard deviation, on the other hand, indicates that the data in the group are more spread out, and hence are distant to the mean value of the group.
The minimum value that a standard deviation can have is zero. It can never go negative since is a measure of distance from the mean value, and distances can never be measured in negative. It is the square root of the variance of a data set. The advantage of calculating standard deviation over variance is that it is measured in the same units as the data, while the variance is measured in squared terms.
Now we shall tell you here how you can calculate the standard deviation for any data in an easy step-by-step guide. But first, let us tell you the formula for calculating the standard deviation.
The standard deviation of any given data set can be found out using the formula
In this, sum means “sum of”, x is a value in the data set, x is the mean of the data set, and n is the number of data points in the population.
While applying the formula in word problems, you might find it bit confusing and difficult to get the correct results sometimes. But here we shall provide you with a step-by-step guide on how you can find the standard deviation for any data set easily.
Here are the steps that you will require to follow to find the standard deviation for any given data set :
- Firstly, find the mean of the given data set
- Then calculate the difference between the square of each observation from the mean value
- Then you need to divide this value by the number of observations
- Now calculate the square root of this value
Now the value which you have arrived at is the standard deviation of the given group. This is the procedure to be followed while calculating the standard deviation for any given data set.
This formula is applicable for smaller data sets or if we want to calculate the standard deviation for a population. In case the data set is so large that it won’t be possible for us to calculate the standard deviation for the whole data set. Hence in such situations, the standard deviation for a sample is calculated.
Here is the formula for calculating the standard deviation for a sample
So using the above-mentioned steps and formulas, you can find the standard deviation for any set of data easily. To help you understand how to calculate standard deviation easily and accurately, we have also provided you with a video tutorial which will break down the steps for calculating the standard deviation and help you understand the steps in a more easier manner.