# How to display data with variation to unsophisticated users?

In my application, students are grouped into classes and each student has a performance metric. I want to be able to show teachers and principals a list of classes, along with an aggregate performance metric for each class.

I don't want to show the mean, because one very high or low performing student skews this. I don't want to show the median, because this basically discards the very high or low performing students entirely, and I want to capture the contribution of these students.

More correct would probably be to show a visualization of the mean with standard deviation. Conceivably I could show a little bell curve sparkline to convey this. But even then, I think this would be too sophisticated for many of my users, and it's not a single number that could be used, for instance, to sort the list by "performance".

Is there a better technique for computing aggregate performance into a single number that somehow captures the variance of the data set?

• Although information visualisation and displaying statistics is in the scope of this site, you might get better advice on calculating the single value needed at Cross Validated Commented May 11, 2020 at 12:00
• Agreed, but even if there isn't a better statistical technique, I need a good way to represent the statistics I've got. Commented May 14, 2020 at 15:21
• Hi Josh. I feel that the "single number" and the "captures the variance" goals are at odds with each other. Your instincts to use a bell curve sound spot on to me. Simply add a single line callout with your aggregate number and let the curve communicate the variance. Commented Jun 23, 2020 at 13:42

Did you consider giving median with a label

• very uneven (red) : std > 4
• uneven (orange) : std > 2
• homogeneous (green) : std <= 2

Sometimes if you draw the statistical distribution, it shows two maxima, showing that there are two groups of students. This might also be an interesting indicator.

When I was in prep' school in France one teacher was very alarmed because the average was increasing but the students were splitting into two categories (high-level increasing, low-level decreasing) showing two very different student types (maybe discouraged or boosted by pressure).

According to me, you should show this curves but after a click, or on user demand if it is a website. As your user become more and more expert with your tool you can start introducing your statistics at first sight.

Example

I put a color on each label, but you should define with your users what event is to be red or green. I put my personal point of view on the colors (I personnaly think that classes of level are better).

• This is an interesting idea. Do you have any example images showing this kind of visualization? Commented Jun 23, 2020 at 14:16
• Added sketch to the main message :) Commented Jun 23, 2020 at 16:14