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I'm creating a report with a KPI that I here illustrate as the share of students passing courses. This KPI has a goal of 90 %.

Given this data

Filter: All courses
Period  |   # Students  |   # Pass
--------------------------------------------
2014-1  |   3511            |   2458
2014-2  |   3454            |   2521
2015-1  |   3522            |   2641
2015-2  |   3508            |   2701
2016-1  |   3595            |   2768
2017-2  |   3590            |   2878

I would create report with a line chart based on this table

Filter: All courses
Period      |   % Pass
(x axix)    |   (y axix, line)
------------------------------
2014-1      |   70
2014-2      |   73
2015-1      |   75
2015-2      |   77
2016-1      |   77
2017-2      |   80

I'm ok with this report. However, given the user of the report now drills down to Stats-101, this is the data that the report would be based on:

Filter: Stats-101
Period      |   # Students      |   # Pass
-----------------------------------------------
2014-1      |   15              |   7
2014-2      |   20              |   10
2015-1      |   21              |   12
2015-2      |   5               |   5
2016-1      |   22              |   15
2017-2      |   35              |   28

The line chart would be based on this

Filter: All courses
Period      |   % Pass
(x axix)    |   (y axix, line)
------------------------------
2014-1      |   46
2014-2      |   50
2015-1      |   48
2015-2      |   100
2016-1      |   68
2017-2      |   80

The variation is of course much higher since the number of students is smaller. How can I make it clear that the variations are likely to be caused by the small number of students?

Here're my thoughts on two possible solutions.

1. Include both [% Pass] and [# Students] in the chart

Filter: Stats-101
Period      |   # Students          |   % Pass
(x axix)    |   (y axix left, bar)  |   (y axix right, line)
-----------------------------------------------
2014-1      |   15                  |   46
2014-2      |   20                  |   50
2015-1      |   21                  |   48
2015-2      |   5                   |   100
2016-1      |   22                  |   68
2017-2      |   35                  |   80

2. Use some kind of margin of error?

Filter: All courses
Period      |   % Pass          | % Pass lower bound    | % Pass upper bound
(x axix)    |   (y axix, line)  |   (y axix, line)      |   (y axix, line)
-----------------------------------------------------------------------------
2014-1      |   46              |   ??                  |   ??
2014-2      |   50              |   ??                  |   ??
2015-1      |   48              |   ??                  |   ??
2015-2      |   100             |   ??                  |   ??
2016-1      |   68              |   ??                  |   ??
2017-2      |   80              |   ??                  |   ??

I'm not good at statistics, so I don't know if the second alternative is viable.

Edit: This seems like a sollution to altenative 2, https://stackoverflow.com/questions/13062398/how-to-avoid-impression-bias-when-calculate-the-ctr

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  • $\begingroup$ "Making it clear" depends on your audience. A statistician, for instance, might be comfortable plotting the counts on a square-root axis, where there will be no visual differences in variability no matter what the size of the group. Could you therefore describe your intended audience? $\endgroup$
    – whuber ♦
    Commented Feb 10, 2017 at 13:55

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