*(This article was originally published September 9, 2012, edited July 21, 2018. Because of the move toward standards-based grading (yay!), the utility of the "averaging" methods listed here are now arguably nil, so though the time for this article's usefulness is past, some may find it interesting anyway.)*

Before the current push toward standards-based grading, I had always had difficulty accepting the traditional 100 point grading scale. Poor performance resulting in **"F" grades can severely affect averages**, especially when the score is a "big F" (below 50%). **I usually gave students at least 50% or 55% in a grading program** so it would register as an "F" but **would not kill their chances** of ever getting out of the "F" range.

After discussing report card grading methods with colleagues at my school, **I decided to investigate different methods** of finding central tendencies of scores. I had no idea how many different ways there are to find central tendencies! I read, I computed, and now I comment.

To see how the methods of finding central tendencies stacked up, **I imagined a student with various scores that included extreme outliers**, as can happen in real life. Here are the scores I used to investigate the different methods. **(You can change the scores and "Update" the graph if you are viewing this with a modern browser.)**

I chose to test ten methods of computing a central tendency. These seemed the most appropriate for use in determining grades based on student assessments. The methods are listed by complexity of computation; **the higher on the list and chart, the more complex they are** to compute. Click on a method or scroll down to read more about each method.

**RESULTS:** When I did my investigation,** I plotted the scores and looked at their placement** (represented by the gray circles in the chart above). **My "gut instinct"** for the original set of scores was that **the student was performing at about 77%**. The methods that produced values **closest to my "instinct"** were Distance-Weighted Estimate, Trimean, Truncated Mean (10%), and Median in this case.

After completing all the calculations, I have come to the opinion that **Distance-Weighted Estimate is the fairest method** when using traditional 100% grading scales without low-outlier adjustments. Unfortunately, my preferred grading program, **Jupiter Ed**, does not compute grades using this method. In fact, **NO online, desktop, or mobile apps use this method!** It is not even easily done in a spreadsheet, which many teachers use for keeping grades. So unfortunately, this method, though (IMHO) **the fairest and most accurate representation of student ability based on cumulative assessments, is unavailable** unless computed by hand or by using the form above (for up to ten scores). (If I get enough encouragement, I may try to build a spreadsheet or dedicated web page to use in my grading. If that happens, I will post it on my website.)

Below are my observations and opinions about each method used in my investigation.

** - Jupiter Ed Gradebook does now have two options for computing grades: traditional "Average" (Arithmetic Mean); and "Summative", using the average of the latest 20% of grades entered.*

**Distance-Weighted Estimate
PRO:**

**Geometric Mean
PRO:** Good for

**Harmonic Mean
PRO:** This method

**Trimean
PRO:** Finds the

**Midhinge
PRO:** This finds the

**Winsorized Mean
PRO:** This method

**Truncated Mean**

Virtually the **same benefits and limitations as Winsorized Mean**. See above.

**Midrange
PRO:** Finds the

**Arithmetic Mean
PRO:** The is the one we teach our students in school. It is also helpfully

**Median
PRO:** Another one we teach our elementary students, so it is also

(Last modified:07/21/2018)

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