## What is Standard about Deviation?

### By Maggie Klenke

Standard deviation is a useful statistical tool for analyzing training scores or quality evaluation marks. Whenever the concept of standard deviation is mentioned, I see a lot of eyes rolling. But the good news is that this useful calculation is really easy, especially done in a spreadsheet program like Excel.

What is it and why would you want to use it? By definition it is a measure that is used to quantify the amount of variation or dispersion of a set of data values. If you have a bunch of numbers that you want to analyze, it is one of the tools that will help you to understand how widely the data points spread from the top to the bottom and how tightly they cluster around the average. The distribution can be visualized on a graph that has the appearance of a Bell. It looks a lot like the distribution that teachers use in school to give most of the students a C, a smaller number a B or D and very few an A or F.

The calculation provides a single number that identifies the distribution pattern in the following manner:

- Approximately 68% of all of the data points will be within 1 standard deviation either above or below the mean (or average). These would be the students who would earn a C grade – including C+ and C-.
- Approximately 95% of all the data points will be within 2 standard deviations from the mean. The 13.6% shown in the sections on the graph would be the students receiving a B or D.
- Nearly all the data points will be within 3 standard deviations from the mean. This is represented in the graph by the 2.1% on either end that would be the students who earn an A or F.

Let’s say you have the scores that each student achieved on a post-training test for an important new concept. With 100 students completing the test, the average score is 80%. That tells us that generally speaking the course has been successful in getting the basic concept across to the agent population. But let’s dig a bit deeper. Maybe we want to know what the high and low scores were to understand the spread. We find that the high score was 100% while the low was 35%. That is a pretty wide spread but we can’t tell from this if lots of the students are very low or high (offsetting each other in the average) or if the distribution finds only a few of them in the extreme categories. That is where standard deviation comes in.

By calculating the standard deviation on this data set, assume we find that the result is 7%. That means that 68% of our students scored between 73% and 87% (by adding 7% and subtracting 7% from the average). Most of the rest scored between 66 and 94%. So it seems that the low of 35% is a real outlier and those few students who scored below 66% probably need some additional coaching. If the standard deviation is high, then we have a more wide-spread problem that may require a different approach.

One of the most common applications of standard deviationis in the quality assurance process when calibrating scores. If 10 supervisor/quality assurance analysts all score a single call, we want to know how closely the resulting scores are to one another. It is important that the standards be defined clearly enough that it doesn’t matter who scores the call, the score will be roughly the same. Tracking the standard deviation of the scores from the calibration team helps to determine if the standards are clear or if they need some more work.

Now that we see how this kind of calculation might be useful, how is it done? The easiest way is with a spreadsheet like Excel. These are the steps:

- Enter all of the numbers to be analyzed in a column or row in the spreadsheet.
- Using the AVG function, you can calculate the average or mean of this data (this is not required to do standard deviation by will be helpful when understanding the results).
- Choose any open cell and select the STDEV function. You will find this under the AUTOSUM character at the top of the spreadsheet where other formulae are stored. When you select this function, the system will ask you to highlight the group of numbers to be used in the calculation. You want to highlight all of the numbers in your analysis and click ENTER or OK. The standard deviation will appear in the open cell. (Note: There is also a calculation STDEVP and this is rarely used in call center calculations as it requires that rather than a sample of data, you have the entire population of data. The results are slightly different from STDEV.)

If you really want to know how to do this manually with a calculator, you can search Excel help, Wikipedia, or other sources for the details – I won’t bore you with them in this article.

This is a useful tool to apply to the plethora of data that we have in call centers. It is quite helpful in analyzing a wide variety of statistics across a group of agents including such things as AHT, absenteeism, quality scores, test scores, etc. It reduces the analysis of the variation to a single number. Using this single number, it is easier to track trends in managing these performance statistics.

Give it a try and you will likely find it is easy to do and a great help in managing your operation by the numbers.

*Maggie Klenke, co-founder of The Call Center School, is a frequent contributor to QATC publications and programs. She can be reached at maggie.klenke@mindspring.com.*