Understand standard deviation

When you view data in Zylinc Advanced Statistics, you may come across the term standard deviation, for example in connection with average answer times for a queue.

Standard deviation is an expression of the variation in a group of data. In other words: how much the individual pieces of data in the group differ from the average of the group.

The standard deviation thus tells you how much you can trust the average to be representative of the individual values behind the average.

If you have a low standard deviation, you can trust the average to be pretty accurate.

Example: The average answer time for a queue is 10 seconds, with a standard deviation of 0,7071067812. That's a low standard deviation, and in fact the individual answer times behind the average were: 9 seconds, 10 seconds, 10 seconds, and 11 seconds. In this case, the 10-second average is pretty representative of the individual answer times.

If you have a high standard deviation, it's a sign of a large spread in the group of data. In that case, the average is still an average, but it isn't very representative of the individual pieces of data in the group.

Example: The average answer time for a queue is 10 seconds, with a standard deviation of 7,71362431. That's a high standard deviation, and in fact the individual answer times behind the average were: 2 seconds, 3 seconds, 15 seconds, and 20 seconds. In this case, the 10-second average isn't very representative of the individual answer times.

In the examples in the previous we looked at the standard deviation of average answer times for a queue. A high standard deviation meant that the individual answer times differed a lot from the average.

Imagine if those answer times were from a queue that was handled by reception staff. Maybe the high standard deviation of average answer times could simply be because the reception staff were sometimes busy with face-to-face inquiries, so that they couldn't answer the phone quickly.

If the high standard deviation had instead been related to average talk times on a queue, it might have been a sign that the calls varied greatly in nature and complexity. In that case, you should perhaps re-think the purpose of the queue, and perhaps set up separate queues for the different types of calls.

The more you know about the organization that the data comes from, the better you'll be able to interpret the data and make informed decisions. That's why the above are only suggestions.

Let's take a simple data set of four numbers:

2, 3, 15, and 20.

That's all the data we have, so we call it our population. If the four numbers were only a small snapshot of a larger set of data, we'd call it a sample, in which case we'd use a slightly different calculation method than the one that we're going to use in the following.

Now, how many numbers do we have?

4

We call that the count.

What's the sum of the numbers?

2+3+15+20 = 40

What average do we get when we divide the sum (40) by the count (4)?

40/4 = 10

Now, take our four numbers and subtract the average (10) from each of the numbers. We end up with what we call the differences:

-8, -7, 5, and 10

Now, square each of the differences. We end up with what we call the squared differences:

64, 49, 25, and 100

Find the sum of the squared differences:

64+49+25+100 = 238

Now, take the sum of the squared differences (238) and divide it by the count (4): We end up with what we call the variance:

238/4 = 59,5

Lastly, find the square root of the variance, and you have the standard deviation:

√59,5 = 7,71362431

You can try out this method yourself with one of the many freely available standard deviation calculators, for example the one on MATHisFUN, which also explains what to do if your data set is a sample rather than a population.