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[Assessment Literacy Video Series] Explaining Standard Deviation

[Assessment Literacy Video Series] Explaining Standard Deviation

Our assessment literacy video series aims to demystify, unpack, and connect assessment concepts and principles to help you make more sense out of your assessment data. Maybe you’re just learning the ropes of some of the more complicated metrics reported in educational assessments, or perhaps you’re hoping to see how an assessment concept applies to Edmentum’s suite of assessment programs. Either way, let our top-notch research team of former educators and subject-matter experts be your guide.

In this video, we’re exploring standard deviation—the statistics term you may (or may not) remember but will find handy when it comes to analyzing your assessment data! Before we dive in, let’s start with a fundamental math concept we all understand—mean, or average. You can find the mean easily by adding up all the scores and dividing by the number of scores there are. Think a little deeper about the mean, however, and you’ll start to realize it masks a lot of what’s really going on with your data. Standard deviation reveals just what the mean might be hiding!  

Let’s take a closer look at what standard deviation is, and then how you can use it to make sense of your data, starting with a simple definition. A standard deviation describes how spread out scores are – in other words, how far they deviate from the average.  Mean scores are very helpful to get a sense of how a group is doing. But when score reports include mean scores without standard deviation, it’s hard to see just how spread out the scores are. That’s because mean is just one number to describe how the entire group of students performed.

Let’s consider two different classes, Class A and Class B, and for simplicity let’s pretend these classes only have five students each. In Class A, students have scale scores from 610 to 645. The mean score is 625. Now let’s look at Class B. Students in Class B have scores as low as 550 to as high as 725 – very different scores from Class A. However, Class B has the same mean score as Class A. Even so, the spread of scores are very different – the scores of Class A are all very close to the mean but the scores of class B are more spread out.

The standard deviation is a way to quantify just how much the scores are spread out and tells you, on average, how far away the scores are from the mean.  We’ll spare you the calculation, but the standard deviation of Class A is about 14 and the standard deviation of Class B is about 78. Since Class B’s scores are more spread out, Class B has a greater standard deviation. This means there is more variation in the Class B results—something the mean would not be able to show you.

On the diagnostic reports for Exact Path, standard deviation is reported inside parentheses next to the average score. You can add and subtract this number from the mean to calculate the range of scores within one standard deviation. On the class results report, teachers can use standard deviation to see how spread out scores are within a single class.

Now when you see mean scores with numbers in parentheses after them and labeled SD, you’ll know what’s really going on! Averages can be deceiving, but the standard deviation will help you get a sense of what the distribution of scores looks like. We hope you are as excited as we are to go check out your own score reports and apply your knowledge of standard deviation! 

Interested in more assessment literacy topics? Check out our Edmentum Assessment Literacy video series, and continue to follow along on the blog as we dig deeper, making you assessment experts along the way! Want to learn more about Exact Path? Get more information about our award-winning program on our website.

audra.kosh's picture

Dr. Audra Kosh began her career in education as an eighth-grade math teacher. After transitioning out of the classroom to pursue her passion for research, Audra completed a Ph.D. in Learning Sciences with a focus on educational measurement and mathematics education at the University of North Carolina at Chapel Hill. Now working as a Research Scientist at Edmentum, Audra does psychometric analyses and assessment research for Edmentum’s suite of assessments.

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