Standard Deviation SD: Explained

What is it, how to calculate it, formula, why it's important

Welcome to my world! The world of finance where everything seems confusing, especially the terminologies. However, we cannot avoid the use of these financial terms in our daily lives because they give us an accurate description of a situation. Today, I’m going to talk about one such term, which is standard deviation, or as we financial people call it, SD.

Standard deviation is a statistical measurement that calculates the amount of divergence or variation from an average. In other words, it’s the measure of the spread of data and how widely they are distributed around the mean. Sounds complicated, but don’t worry, I’ll explain everything step by step.

Why Is Standard Deviation Important?

Let's get straight to the point and answer this question. Standard deviation is essential because it helps to interpret and compare data. By calculating the standard deviation, we can determine how much variance there is between different sets of data. It’s not just about telling us the average; it also shows us how much the data deviates from that average.

For example, imagine that we have two companies. One company has a yearly revenue of \$1 million, and the second company has a yearly revenue of \$1 million. Without standard deviation, we assume that both companies are on the same level. However, when we add standard deviation to this equation, the picture becomes clearer.

If the standard deviation of the first company is low, say around \$10000, it means that the company’s revenue has been consistent over the years. On the other hand, if the second company has a higher standard deviation, say around \$500000, it means that the company’s revenue is not stable and fluctuates a lot.

Therefore, standard deviation is a critical measure for investors because it helps identify potential risks and opportunities.

How To Calculate Standard Deviation?

Enough talk! Let's get down to the nitty-gritty of how we calculate the SD. The formula is pretty straightforward, and I promise you won’t need to be a mathematical genius to understand it. Here is the formula:

SD = √Σ(x – μ)²/N

Broken down, here’s what each term represents:

• SD = Standard deviation
• x = Value of each observation
• μ = Mean of all observations
• N = Total number of observations

To make things easier, let me take you through an example of how to calculate the standard deviation. Let's assume that you want to find out the average grade of a class of 30 students. The grades range from 60-100%, and you got these results:

• 60%, 65%, 70%, 75%, 80%, 81%, 82%, 83%, 85%, 85%
• 86%, 86%, 87%, 87%, 88%, 88%, 89%, 90%, 90%, 92%
• 92%, 93%, 94%, 95%, 97%, 98%, 99%, 99%, 100%

Calculate the mean of all observations by adding all the grades and dividing by the total number of observations:

Mean = (60+65+70+75+80+81+82+83+85+85+86+86+87+87+88+88+89+90+90+92+92+93+94+95+97+98+99+99+100)/30 = 87.1667%

Great! Now that you have the mean, let's calculate the SD:

```       ___________________
\/ Σ(x - μ)² / N```

SD = √((60 - 87.1667)² + (65 - 87.1667)² + ... + (100 - 87.1667)²)/30

SD = 12.98%

There you have it! The SD for this data set is 12.98%, which means that the grades of the students are scattered around the mean by almost 13 percentage points. If you want to know the results of this calculation without doing the math, many standard deviation calculators are available online to use for free.

Types of Standard Deviation

Before we conclude, I want to discuss the two types of standard deviation. Yes, you heard me right! There are two types of SD, population standard deviation, and sample standard deviation.

Population standard deviation is used when we want to know the standard deviation of the entire population. For example, if we want to calculate the standard deviation of the height of all men in the world, we would use the population standard deviation since we want to know the SD of the entire population.

On the other hand, sample standard deviation is used when we want to know the standard deviation of a subset of the population. For example, if we want to know the standard deviation of the heights of 100 men out of the entire population, we would use the sample standard deviation.

Conclusion

Standard deviation, or SD, is a crucial statistical measurement in the world of finance. It helps us understand and compare data by measuring the deviation from the mean. By calculating the standard deviation, we can identify potential risks and opportunities and make informed decisions.

Don't be afraid of those tangling statistical equations; it's just like cooking! You need to follow the recipe. Standard deviation may look complicated, but once you get the hang of it, it is quite easy, and it will help you make smarter financial decisions.

And there you have it! Now you can go out into the world and show off your newfound knowledge about SD. Who said that finance can’t be fun!