Standard deviation is a mathematical concept.

Many professionals are intimidated by this as it involves mathematical calculations; however, you should understand the significance of this important concept. Once you understand the practical application of standard deviation and know the calculations, you will not forget it.

Let’s dive in.

## Standard Deviation

Standard deviation is the “Mean of the Mean.” It tells you how the data are spread.

The mean is the average of the given numbers.

First, let’s analyze a mathematical example of this concept.

### Example of Standard Deviation

Your class has five students, and the height of each student is as follows:

First student = 150 cm

Second student = 160 cm

Third student = 170 cm

Fourth student = 165 cm

Fifth student = 155 cm

Calculate the standard deviation.

To calculate the standard deviation, you need the mean and variance.

Mean = (150 + 160 + 170 + 165 + 155) / 5

= 160 cm

To find the variance, subtract this “mean height” from each student’s height, square it, add them together, and take the average.

Variance = [(150 – 160)2 + (160 – 160)2 + (170 – 160)2 + (165 – 160)2 + (155 – 160)2] / 5

= [100 + 0 + 100 + 25 + 25] / 5

= 250 / 5

= 50

Hence, the variance is 50.

Standard Deviation = Square Root of Variance

Standard Deviation = Square Root of 50

= 7.07

Hence, the standard deviation is 7.07 cm.

You might wonder how useful this data is.

These data are essential because they give you the following information:

- The average height of students is 160 cm (mean).
- The height of most of the students varies from 152.93 cm (160 – 7.07) to 167.07 cm (160 + 7.07).

The image above shows the standard deviation for five students. The vertical lines show the height of each student (e.g., 150 cm, 160 cm, etc.). The blue line is the average (or mean) line, and the maroon lines represent the standard deviation.

You can see that the standard deviation lines are drawn above and below the average line, and the height of most of the students lies between these two maroon lines.

Put simply, you can say that the height of most students is between 152.93 cm to 167.07 cm.

Let’s revise the whole procedure once again:

- Calculate the average height of the students.
- Subtract the average height from the height of each student and then square it.
- Add them together and take the average.
- Now take the square root.

### Important Note

I used population-based data in my example; by this, I mean there were only five students in the class.

However, if you select sample data, i.e., choosing a few random numbers from a large data pool, you will have to divide the variance by (N-1), where N is the number of samples. In other words, if the class has hundreds of students, and you select five, you will divide the variance by (5 – 1) or 4.

You may wonder why we are squaring a number if we take the square root of it.

There is a reason for this calculation; the positive and negative numbers cancel each other out if we add the difference.

### Application of Standard Deviation

Standard deviation is used in analyzing data, and it is a vital tool for industries, especially for clothing manufacturing.

Standard deviation provides information about what size is small, normal, medium, large, or extra-large. Based on the result, the manufacturer sets the size of pants, shirts, t-shirts, etc.

### Summary

Standard deviation is a statistical analysis tool that helps industries understand parameters for the whole population by analyzing a sample of data. Although this technique involves mathematical calculation, the concept is straightforward, and standard deviation tells you how your data are spread. Based on this information, you can develop and market your product.

I hope the standard deviation is clear to you. If you still have doubts, send me a message through the comments section, and I will reply to you.

Standard deviation is an essential concept from a PMP perspective. You may see a question from this topic on your exam.