How To Find Standard Deviation

So, there I was, sitting in my stats class, staring at a problem that looked like it was written in a language from another planet. "Find the standard deviation," it said, as if that was supposed to mean something to me. I mean, I knew what deviation was, sort of - it's like when your friend cancels plans at the last minute, right? But standard deviation? That was a whole other story.

Anyway, long story short, I ended up acing that stats class, and now I'm here to share my wisdom with you. You're welcome, by the way. So, let's dive into this standard deviation thing, shall we?

What's the Big Deal About Standard Deviation?

Alright, let's start with the basics. Standard deviation is like the spread of your data. It tells you how much your numbers are deviating from the average. In other words, it's the average of how far each number is from the mean. Still with me? Good.

Now, why is this important? Well, imagine you're trying to decide between two jobs. One offers $30,000 a year with a standard deviation of $5,000. The other offers $35,000 a year with a standard deviation of $10,000. Which one would you choose?

If you said the first one, you're not alone. But hold on a sec. The first job might have a lower average salary, but the salaries are more spread out. There could be people making $25,000 and others making $45,000. The second job, on the other hand, might have a higher average, but the salaries are more clustered around that number. So, it's not just about the average, it's about the spread too.

How to Calculate Standard Deviation

Now, let's get our hands dirty. The formula for standard deviation is pretty straightforward. It's the square root of the average of the squared differences from the mean. Yeah, I know, it sounds scary. But don't worry, I'll break it down.

First, you find the mean (average) of your data. Let's say you have the following numbers: 4, 9, 16, 25, 36.

How To Find Standard Deviation X at John Keys blog

Add them up: 4 + 9 + 16 + 25 + 36 = 90

Divide by the number of values (5 in this case): 90 / 5 = 18

So, the mean is 18.

Next, you subtract the mean from each number and square the result:

• 4 - 18 = -14, squared is 196
• 9 - 18 = -9, squared is 81
• 16 - 18 = -2, squared is 4
• 25 - 18 = 7, squared is 49
• 36 - 18 = 18, squared is 324

Now, you add up those squared differences: 196 + 81 + 4 + 49 + 324 = 654

How to Calculate Standard Deviation: 12 Steps (with Pictures)

Divide that sum by the number of values (5 again): 654 / 5 = 130.8

Finally, take the square root of that result: √130.8 ≈ 11.4

And there you have it! The standard deviation of your data is approximately 11.4.

But Wait, There's More!

Now, you might be thinking, "That's all well and good, but what if my data isn't in the same units?" Well, my friend, that's where the population standard deviation and the sample standard deviation come in. The population standard deviation uses the population mean and the sample standard deviation uses the sample mean. The only difference is in the denominator of the formula. For the population standard deviation, you divide by the number of values (N), and for the sample standard deviation, you divide by one less than the number of values (N-1).

And that, my dear reader, is standard deviation in a nutshell. It's not as scary as it sounds, I promise. Just remember, it's all about the spread of your data. Now go forth and calculate!