This is a "stand-alone" version of an article on my main website.
# Methods of Finding Central Tendencies for Report Card Grading

I have 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, **JupiterGrades**, 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.

**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

**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