# Really Simple Statistics: What is a standard deviation? #MRX

Welcome to Really Simple Statistics (RSS). There are lots of places online where you can ponder over the minute details of complicated equations but very few places that make statistics understandable to everyone. I won’t explain exceptions to the rule or special cases here. Let’s just get comfortable with the fundamentals.

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Standard deviations are massively popular in all aspects of market research reporting. Any time someone tells you an average number, they’ll probably tell you  what the standard deviation is at the same time, even if you didn’t ask for it. At it’s most basic level, a standard deviation is a number that tells you how similar a set of numbers is.

For now though, let’s forget about all the technical language and think about a casual application. In your immediate family, most of the women are probably similar to each other in terms of their height. If your mom is 5 foot 3, chances are that many other women in your family are somewhere around 5 foot 3, and in fact most of them are probably within an inch or two of 5 foot 3. The “normal” woman is about 5 foot 3 and there is very little differentiation or deviation among the heights. The deviation is small.

On the other hand, get out the wooden ruler you’ve saved since public school, the one with your 4ever true love engraved on it, and hold it up to their hair. Some of the women have really long hair, others have shoulder length hair, while still others have short and snazzy hair. There’s a lot of  differentiation, a lot of disagreement, a lot of deviation in their hair lengths. Sure the average or normal length might be 8 inches, but the deviation from the norm could easily be 8 inches. The deviation is large.

In the market research space, you can look at standard deviations in a similar way. It can be interpreted as the amount of disagreement among people’s opinions. Let’s consider 100 answers to a purchase intent question asked on a five point scale from Definitely Will Buy all the way to Definitely Will Not Buy.

1. If 50 people answered definitely will buy and 50 answered definitely will NOT buy, that’s a big difference among the answers, a lot of disagreement, a lot of differentiation. Half of the people are checking off the 5 and half of the people are checking off the 1. People haven’t come to any consensus on whether they agree or disagree. In technical words, that clear disagreement indicates a wide or large standard deviation. These wide standard deviations make our work as market researchers more difficult. It’s hard to recommend a new product when people can’t agree on whether they would buy it.
2. But, if 90 people answered definitely will buy and 10 people answered probably will buy, there’s a lot of agreement there. 90% of the people are checking off the 5 and 10% of people are checking off the 4. People are generally agreeing with each other. They pretty much all intent to buy though some are a little more sure about that purchase than others are. That agreement reflects, inversely, very little differentiation, very little disagreement. It indicates a very narrow or small standard deviation. This is what market researchers love to see. We have a clear answer to our question and can proceed to recommend a product that most people would like to buy.

So here’s the general scoop:

• Small standard deviation = Lots of agreement among the opinions
• Large standard deviation = Lots of disagreement among the opinions

It’s that simple!

### 6 responses

1. Nice explanation. I like to use the word “consistent” when talking about standard deviations. More consistent means smaller standard deviation. We are clearly on the same wavelength.
I also like how simple this is. I recently took a look at an on-line course that said it was simple. It included using R. Not my definition of simple.

1. LOLOLOLOL! R=simple. Sure, And painting a Picasso is simple.

2. Mutahir Hussain

Lovely Annie, It is a really easy, a non stat person like me can easily understand these terms.

1. I’m glad you found it useful. Keep on statisticing! 🙂

3. Annie, I really enjoyed all of the Really Simple Statistics post. They are great and have provided me ideas to explain to my clients when they ask the same questions.

1. I’m so glad to hear it! Glad you found them useful.