While average and median GRE scores can be similar, the nature of how each is calculated can cause the disparity between them to grow when results are skewed toward one end of the score range. Learning how an average and a median are calculated can help you understand why the Educational Testing Service -- the GRE's administrator -- provides only average and not median scores to assess your performance on the GRE.

## Average Calculations

An average, also known as a mean, score is calculated by adding all score results for a given number of test takers. You then take this sum and divide it by the total number of test takers to arrive at the average, or mean, test score. Using a hypothetical sample set of 2, 3, 5, 7, 8 and 10, for example, your average would equal (2+3+5+7+8+10) ÷ 6, or 5.83. This result reflects the exact midpoint of all combined numbers, or scores.

## Median Calculations

Calculating the median involves finding the midpoint number in a given set of figures. This involves sorting all scores in order of smallest to largest and then adding the total number of scores, not score values, together. If this score number if even, you locate the two middle numbers and take their average to find the median. For example, when given the numbers 2, 3, 5, 7, 8 and 10, your two middle numbers are 5 and 7, which, when averaged, resulted in 6 as the median, which is nearly identical to the calculated average.

## When Average and Median Disagree

This median calculation can become skewed in comparison to the average when the same or similar figures become predominant in a series. For example, the average of the set of numbers 2, 3, 5, 6, 8, 8, 8, 9, 9 and 10 is 6.8. The median of this series, however, would be 8, illustrating the growing discrepancy between average and median results as data points become heavier toward one end of your data range. You can extrapolate how dramatic this skew would become given a full data set of GRE test scores for thousands of test takers, making the calculated average a more precise midpoint of score results.

## Average and Median GRE Scores

While ETS does not publish a median score for the GRE exam, it did report the average scores for over 900,000 test takers from 2011 to 2013. According to its report, those who sat for the exam scored an average of 150.75 out of a possible 170 points on the verbal reasoning section and 151.91 out of 170 points on the quantitative reasoning section. In addition, test takers received a mean score of 3.61 out of 6 possible points on the analytical writing section of the exam.

#### References

- United States Department of Agriculture Natural Resources Conservation Service: Median Versus Average to Describe Normal
- Texas A & M University Chemistry Department: Average, Standard Deviation and Relative Standard Deviation
- Brooklyn College: Calculating the Mean and Median
- Educational Testing Services: GRE: Guide to the Use of Scores 2013-2014

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