Teachers Need to Look at Median Grading

Assessment and evaluation methods are generally left to teachers,
who prefer averaging grades.

The challenge proper grading is to find a single number for that best represents an entire set of scores on different types of assessments. Statisticians refer to this single number as a measure of central tendency. There are three of these measures – the mean, median, and mode. 

The average is the same as the mean. It is easy to understand and perform. The scores are totaled and divided by the number of scores. This more accurately called the arithmetic mean – all scores carry the same weight or importance – as opposed to the weighted mean in which some scores weighted or given more importance than others.

The most widely used method of finding a “grade” is using the arithmetic mean. A simple case would be to find the average for the following scores: 0, 60, 60, 70, 80, 90, 100. The teacher totals the scores and obtains a sum of 460. The sum is divided by the number of scores – 7. The arithmetic mean is 65.1 or 65 when rounded off.

Most teachers have been using the mean forever. It is easy to compute and seems to make sense. It’s one of those things that is just done  in public education. Why make waves? We prolong a lot of practices in education because of the assumption that what has been done should be done.

Median Grading is a Better Way for Data like Student Scores

The crux of the problem is that the mean is not recommended when data is affected by outliers, which are extreme scores that are substantially different from most of the scores. In the example above the zero is an outlier and they usually are. When outliers skew data, the median is a better measure of central tendency. If you need a reasonable explanation for this, then look at the scores above – most are above the average score obtained. Also, four of the seven scores are above passing, but the average is a failing score.

The median is simply the middle score obtained after arranging the grades in order from low to high. The median for the list above is 70 – five points better. When there is an even number of scores, the median is the average of the two middle numbers. The median is not a “trick: designed to raise scores, but a valid statistical measurement.

Assume the graph shown below is a students distribution of scores with most scores in an "expected" range –  60 to100, with low scores on the left. On the left there are a couple of scores below 10. Notice how the average – that's the X with the little line over it. Notice how it is the lowest of all three measures – modes are rarely a part of evaluation. 

0      10                                          66.8   70.1

The use of the average penalizes students with low outliers. Teachers may have an attitude that precludes accepting the reality of the outlier effect. They may feel that any student who gets a zero has fairly earned it and its effect on the average score. However, zeros beg the question of “How was the zero achieved?” It may have been simply given for missing work. If it is legitimately earned when an assessment is taken, then the teacher should consider its value as diagnostic. I.e., when students honestly make zeros there may be a serious problem interfering with learning. Find out what the problem is and act accordingly.

Some Schools, Districts, and Teachers Manage the Outlier Problem Arbitrarily

Of course high scores can be outliers if a student typically earns 40’s and 50’s consistently, but that is rare. If it happens, that should also call for diagnosis and intervention. Years ago, some schools and district adopted policies that essentially banned zeros and very low scores. It was an arbitrary way to “simulate” median grading. The averages tended to be a bit higher and closer to the median. Statistically, the truth is that student grades had been incorrectly computed and usually to their detriment.I was teaching when the change came to my district and the policy was not popular – it was viewed as giving students an unfair break. This the archaic attitude that grades serve as rewards and punishments. Grades are for evaluation!

Teachers often adopt a policy of dropping the lowest grade because of their recognition of the outlier problem. The Olympic scoring method that drops the highest and lowest score is done for the purpose managing outliers.  

Recording too many grades can make median grading problematic. If 50 or 60 grades are involved then finding the median is a chore. However, if teachers record only summative grades – i.e., tests and quizzes – there will likely be a much smaller number of scores and median grading can be faster than finding a mean.

Teachers Can Improve Grading Accuracy and Motivation with Median Grading

For most sets of student scores, the median will produce a higher score than the mean. In fact the difference in points can be large enough to determine whether or not a student passes or fails. Also, higher grades tend to motivate better than lower grades.

Consequently, the use of median grading could have a duel impact on final grades ­– one is the result of usually raising grades, and the other is due to the effects of positive motivation.

A disadvantage of the median is that it does not have a formula. The median has to be determined by taking the time to find the middle score. Spreadsheet programs like Excel can produce medians and means. Some grading programs can produce a variety of data including the mean and other statistical data.

Teachers might wish to compute the grades of a few different students using medians versus the mean. When computing the median write tests three times, quizzes two times, etc., or some similar method allowing for the different values of various assessments – it would not be a good idea to count a test as much as a homework assignment.

Grades are supposed to give an accurate appraisal of student progress. There are numerous methods of arriving at this “magic number,” and many are not based on viable mathematical practices. The median offers a correct and direct way to add much needed consistency and fairness to the evaluation process.