# Standard Deviation and Marketing – How, Why?

By**What Is Standard Deviation? **

Standard deviation is used to measure the *average difference* between *the individual numbers* that make up your data sets’ arithmetic *mean* (mean being the average or center) and their mean value.

**Example 1:**

You have 4 numbers; 7,10,6, and 7 again, their mean ((7+10+6+7 =30)/4) = is 7.5, but their standard deviation is 1.5 (I’ll explain later how to calculate the standard deviation). So the average of the numbers is 7.5 plus or minus 1.5. You will usually see it reported as 7.5 +/- 1.5. The addition of the standard deviation number enables you to tell a more complete story of the data spread in the data set allowing viewers to see the average difference between the individual numbers that make up your mean and their mean value.

**Example 2:**

Below is a more of an extreme example, but it shows you the importance of knowing what the standard deviation is when reporting on an average of a data set:

Now let’s assume you are doing a poll of all 4 people that work in your small office (including yourself) because you want to know the average number of pens everyone in your office has at their desk. The answers you get are 5,7,10, and 200 pens. Their mean (or average) is 55.5, but their standard deviation is 83.4.

By reporting it as the workers in your office have an average of 55.5 plus or minus 83.4 pens really lets the reader of the data know that data set has a large spread. Although the average is 55.5 pens, it really doesn’t give any insight to the fact that 1 of your coworkers has 200 pens while the rest have less than 10 pens.

What happens if all the numbers in your data set are the same? Well, if all 4 people reported that they had 2 pens each, then your average or mean would be 2 pens with a standard deviation of 0 because all of the numbers that make up your data set are the same as the average number itself, so there is no deviation from the average for the number of pens each individual has.

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**Why you need to understand standard deviation in Marketing and Optimization?**

So now you’re thinking, OK, so how is this applicable to Marketing and Optimization?

Let’s say you want to know the Average Order Value (AOV) of a particular channel that sends visitors to your eCommerce site (some people dont like to use standard deviation when working with value, so you could replace AOV with average order size in this example). For simplicities sake (to keep this explanation short- so go along with this) let’s pretend that you have 10 orders (yes this is small, but again to keep this simple) during the period you are viewing – 4 orders at $99, 1 order at $1,499, and 5 orders at $5. Your AOV is $192 (all 10 numbers added up and divided by 10), but the standard deviation is $437.91.

Telling someone that you’re AOV is $192 really does disservice to the real truth of your order values. By stating that your AOV is $192+/- $437 lets the viewer take a step back and realize that there is an order or orders that are spread out far from the mean. Yes, some people will remove the outliers, etc., etc., but if you do that, you should provide that as an additional metric alongside the mean and the accompanying standard deviation – but that conversation is better set for a different time (kind of like discussing politics as you will get all sides and opinions).

Can you think of other areas where knowing this in your marketing would really help understand the numbers better? Rarely do you have such small data sets that you want to base decisions on for marketing’s sake as I have presented here for simplicities sake. But imagine if you had 1,000 numbers to report on that were all over the place with varying spreads? How about comparing performance of various test panel results in your online testing?

The closer the individual numbers are from your mean, the smaller the standard deviation will be. And, the further the individual numbers are from your mean, the larger the standard deviation will be.

**How to Calculate Standard Deviation in Excel**

In Excel to get to standard deviation is for the most part really simple:

*If your data is from a SAMPLE, use this Excel standard deviation formula (a sample is a portion of the total population, i.e. 300 employees chosen randomly, 500 orders chosen randomly):*

**=STDEV(Cell Range)
** I should note that you don’t want to actually type in

*Cell Range*, but put in the cell range or individual cells that you are your data set: so if you have your data in cells A1, A2, A3, and A4, then you would use the formula

**to get your standard deviation.**

*=STDEV(A1:A4)**If your data is from a POPULATION, use this Excel standard deviation formula (a population is the total population, i.e. all employees at work, all orders received): *

**=STDEVP(Cell Range)
** I should note again that you don’t want to actually type in

*Cell Range*, but put in the cell range or individual cells that you are your data set: so if you have your data in cells A1, A2, A3, and A4, then you would use the formula

**to get your standard deviation.**

*=STDEVP(A1:A4)*

**Hand Calculating Standard Deviation **(not advised for large data sets)

- 1. Add up all the numbers in your data set to get a total
- 2. Take that total and divide it by how many numbers you have in your data set (this is your
*mean*) - 3. Subtract the difference of each number from the
*mean*and square each difference - 4. Add each of the squared differences together
- 5. Take the sum of the squared differences in step 4 and divide it by how many numbers you have in your data set (this number is your
*variance*) - 6. Take the square root of the
*variance* - 7. The answer is your
*standard deviation*

**Online Standard Deviation Calculator**

A nicely done online standard deviation calculator can be found at* Math is Fun* Standard Deviation Calculator page. Definitely take some time to play with this; well I think its fun at least.

So the next time someone gives you some “average” ask them what the standard deviation is and you probably will throw them what they think is a curve ball, but it will give you much clearer insight into what the real info is behind that average. And for your own marketing purposes, it will give you a better understanding of your data and those who need to view it (after of course explaining what standard deviation is and why it’s important!).