# Is this a good use of Standard Deviation on data that is not normally distributed?

I have a series of numbers ranging from -0.69 to 14.703. These datapoints measure YoY change. I want to create a text descriptor based on where a value falls in a range determined by the Standard Deviation. My mean is 1.13144 and Std Dv is 2.1579. This leaves me with these standard deviation steps, to which I assign a value (i.e. if you fall between the mean and (negative) 1 SD, you are Below Average, between the mean and (positive) 1 SD, you are Above Average, and so on. This the list of values I got the mean and Std Dev from: Nearly every item in this list falls 1 SD below the mean. I know the data is not normally distributed, but I would have expected something a little less skewed. Am I using this correctly?

Edit: Year over Year (YoY) change. I take last year's sales and this year's and find the percent difference.

• Can you explain YoY change? May 18 at 14:57
• Year over Year change. I take last year's sales and this year's and find the percent difference.
– jabs
May 18 at 14:58
• Could you explain why you want to base your classification on the SD while at the same time you recognize the SD might not be appropriate or useful for this distribution? If your underlying problem is to partition the data, then consider reframing it as a clustering problem or, even more simply, just partition the data according to quantiles, such as 0 - 10% ("very low"), 10% - 25% ("low"), 25% - 75% ("medium"), etc.
– whuber
May 18 at 15:04
• A graph would say much more about these numbers than arbitrary binning based on any criterion. I would illustrate, but the data are presented as an image. The graph could be combined with text annotation if something else were known about each value (that isn't confidential). May 18 at 17:09
• Whether the distribution is normal should not be overemphasized. No distribution of data is or can be exactly normal. Everything depends on whether there is a reference distribution that acts as a standard comparison. For example, the exponential has SD equal to the mean, which means that values are expected to vary from about $-1$ SD below the mean to rather more SD above the mean. That's what it is. Use it if it is helpful and not otherwise. Jun 1 at 6:31

You see a similar effect in other outlier-dependent summary statistics like the mean. For example, the mean net worth in the US is nearly $1M, but this is dragged way up a small number of billionaires, so many would view it as a misleading summary statistic. The median net worth is barely \$100k, which most would view as a better summary of the population.