Standard Deviation – Why and How
By Maggie Klenke
As we talk with people in contact centers, there seems to be a lot of concern about “industry averages” and what other people are doing. We have generally taken the position that it really doesn’t matter much what others are doing, but whether are you fully aware of where your performance is now and what you can do to improve it. Using statistical analysis tools can go a long way to helping you understand your current situation and where the best opportunities may lie for improvements, and standard deviation is a good one to start with in your analysis.
So what does standard deviation measure? Essentially, it is an analysis of the “central tendency” of the data or how closely clustered the results are around the average. If you have lots of variation in the data points, the standard deviation number will be high, but if all the numbers are pretty close together, the standard deviation number will be low.
Let’s apply this concept to a couple of call center operations and see how it might be useful. The first is in workforce management as a measure of forecasting accuracy – or how closely the forecast and the actual call volume, handle time (AHT) and/or staffing matched up to what you planned for. Let’s start with the set of data below in terms of the forecast call volume, the actual, and the percentage of error for each day of the week and the total for the week. As we look at the results for this week, we see that we have a 3.9% error overall and most would consider that pretty close. Each day of this week is within 5% as well.
Forecast Volume | Actual Volume | % Error | |
---|---|---|---|
Monday | 3533 | 3601 | .019 |
Tuesday | 2455 | 2544 | .036 |
Wednesday | 2611 | 2723 | .047 |
Thursday | 2990 | 3111 | .040 |
Friday | 2935 | 3078 | .049 |
Saturday | 1028 | 1103 | .073 |
Total | 15,552 | 16,160 | .039 |
Now let’s look at another set of data. In the next table, the total for the week is even closer. There is less than 1%
error for the week. When only the weekly total is considered, this forecaster seems to be doing a magnificent job.
Forecast Volume | Actual Volume | % Error | |
---|---|---|---|
Monday | 3533 | 3494 | – .011 |
Tuesday | 2455 | 3156 | + .286 |
Wednesday | 2611 | 2854 | + .093 |
Thursday | 2990 | 2647 | – .115 |
Friday | 2935 | 2301 | – .216 |
Saturday | 1028 | 993 | – .034 |
Total | 15,552 | 15,445 | – .007 |
But we cannot ignore the fact that the individual days are wildly off in some cases with 28% more calls than expected on Tuesday and almost 22% fewer than expected on Friday. You can imagine the intra-day chaos in this center while supervisors try to round up every available person, cancel meetings and postpone training on Tuesday, and then try to fill everyone’s time productively on Friday.
Looking at just one week of data it is pretty easy to see the challenges here, but when there is a larger quantity of data or a desire to keep a running tally of the results from week to week, the standard deviation calculation can be a great aid. When we start to look at the data by time of day, the quantity of information can be overwhelming, but a single standard deviation number can tell the story pretty succinctly.
Let’s consider another example from the quality assurance operation below. In this case, we are calibrating quality monitoring scores to ensure that everyone who listens to a call and scores it comes up with pretty much the same results. This is critical to the credibility of your QA process. Here are the scores produced by a team of eight QA analysts and supervisors who listened to the same two calls and provided scores on them.
Call #1 | Call #2 | |
---|---|---|
Scorer | Score | Score |
Mary | 97 | 87 |
Joe | 94 | 69 |
Elsie | 95 | 72 |
Mark | 92 | 68 |
Leon | 99 | 90 |
Sue | 93 | 85 |
Lee | 96 | 79 |
Ahmed | 97 | 66 |
Just looking at the data, you can see that the Call #1 scores are relatively close together while the Call #2 scores are not. But once again, it is hard to define that level of variation without some kind of tool.
So let’s apply standard deviation to our two types of data. In the forecasting data, we are interested in the rate of error so we will start with that data as our basis for the analysis. The standard deviation is the square root of the variance. Here are the steps you would use to calculate it manually with a calculator (we’ll show the easy way in Excel next):
The Calculation Steps:
- Calculate the average of all data points.
- Subtract the average from each point.
(Some will be negative numbers.) - Square each number and add them all together.
- Divide total by number of data points.
- Take the square root of that number for standard deviation.
Let’s apply this to the quality monitoring scores for the second call:
- Calculate the average of all data points. (87+69+72+68+90+85+79+66)/ 8 = 77
- Subtract the average from each point.
- 87 – 77 = +10
- 69 – 77 = -8
- 72 – 77 = -5
- 68 – 77 = -9
- 90 – 77 = +13
- 85 – 77 = +8
- 79 – 77 = +2
- 66 – 77 = -11
- Square each number and add them together (remember that squared negative numbers become positive)
- 10 X 10 = 100
- -8 X -8 = 64
- -5 X -5 = 25
- -9 X -9 = 81
- 13 X 13 = 169
- 8 X 8 = 64
- 12 X 2 = 4
- -11 X -11 = 121
- Total = 628
- Divide total by number of data points. 628/8 = 78.5
- Take the square root of that number for the standard deviation which is 8.86
While that is pretty straightforward math, it does require a lot of calculations, especially when you have a ton of data, so let’s do it in Excel.
In this screen shot, you can see all of the steps done individually. First we entered the data in the first two columns. Then we figured the average score in cell B11. This is easy to do using the function located under the E symbol in the tool bar. Using the drop down arrow on the right, select average and it asks you to highlight the items (B3 through B10). The Step 2 variance is calculated in column C by simply subtracting the average in B11 from each of the items in Column B. Step 3 is done in Column D by squaring each number in Column C and the total is added up in D11. Step 4 is completed in D12 when the 628 in D11 is divided by 8 (the number of data points). And the final step is in D13 where the square root of 78.5 is calculated by using the function SQRT.
All of this can be shortcut by just entering the data in Columns A and B and then selecting any open cell to calculate the standard deviation. When you go into the functions list, you will see two options for standard deviation (STDEV). Another option is to calculate the standard deviation of the percent of variance. This overcomes the wide variation in the total volume by day of week and may be a better indication.
As you analyze your data and get your standard deviation numbers, remember that the smaller the number is, the more tightly clustered the data points are. In the case of forecasting accuracy and quality scores, smaller is better. Look for the outliers that are causing the wide fluctuations and work on getting those closer to the average and the standard deviation will continually go down. Set your goals to reduce the standard deviation by a small amount each period and over time you will find ways to achieve significant improvements in your contact center’s performance.
Maggie Klenke was a Founding Partner of The Call Center School. She may be reached at maggie.klenke@mindspring.com.