What Is Median Score?
The median score is the middle value of a sorted list, so half the scores are below it and half above. It is often a better summary of a class than the mean because a few extreme scores do not move it.
Paste your scores to get the median, lower and upper quartiles, IQR, lowest and highest score and the mean. Add one score to see its percentile rank and whether it is above or below the median. A box plot and the sorted list are included.
Below are the formulas, a worked example and answers on percentile rank.
How to Use the Median Score Calculator
- Enter all scores.
- Optionally enter one score to rank.
- Read the median and quartiles.
- Check the box plot.
Median Score Formula
Median position
Percentile rank
Median Score Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| n | Number of scores | |
| Q1, Q3 | Lower and upper quartiles | |
| IQR | Q3 − Q1 | |
| PR | Percentile rank |
Median Score Worked Example
Sorted scores 64, 70, 72, 76, 78, 82, 85, 88, 90, 95 (n = 10) have median (78 + 82) ÷ 2 = 80. For a score of 85, 6 scores are below and 1 equals it, so the percentile rank is (6 + 0.5) ÷ 10 = 65 %.
With the example values loaded in the calculator above, the steps are:
- Sort the scores: 64, 70, 72, 76, 78, 82, 85, 88, 90, 95.
- n = 10 is even, so the median is the mean of the middle two scores (numbers 5 and 6): 80.
- 6 scores are below 85 and 1 equal it, so percentile rank = (6 + 0.5 × 1) ÷ 10 = 65 %.
Result: Median score = 80; Percentile rank of 85 = 65 %.
How to Read a Median Score
The median is the middle score once the scores are sorted. For the ten scores 64, 70, 72, 76, 78, 82, 85, 88, 90 and 95, the median is (78 + 82) ÷ 2 = 80. Half the class scored above it and half below.
The quartiles and the IQR show the middle half. A score of 85 has a percentile rank of (6 + 0.5) ÷ 10 = 65%, which means about 65% of the class scored at or below it. The median is the better summary when a few very low or very high scores would drag the mean.
Where Median Score Is Used
Class results
Find the middle score of a test and the quartiles.
Percentile rank
See where a particular score sits within the group.
Mean versus median
Compare the two for a skewed set of scores.
Reporting
Give the median and IQR along with the range.
Common Median Score Mistakes to Avoid
- Sort the scores first. The median is the middle of the sorted list.
- With an even number of scores, average the two middle values.
- The percentile rank formula used here is (scores below + half the scores equal) ÷ n. Other definitions exist.
- Use the median for skewed scores and the mean for symmetric ones.
Median Score Terms and Definitions
- Percentile rank
- The percentage of scores below a given score, with ties counted as half.
Median Score FAQs
How do you find the median score?
Sort the scores and take the middle one. If there is an even number, average the two middle scores. For 64, 70, 72, 76, 78, 82, 85, 88, 90, 95 it is (78 + 82) ÷ 2 = 80.
What is the percentile rank of a score?
It is the share of scores below it, counting half of any that are equal to it. A score of 85 in this set has 6 below and 1 equal, so (6 + 0.5) ÷ 10 = 65%.
Median or mean for test scores?
Use the median if a few very low or high scores distort the mean. If the scores are roughly symmetric, the two are close and either is fine.
What does the IQR show?
The interquartile range is Q3 − Q1 and covers the middle 50% of scores. It tells you how spread out the typical scores are, without being affected by extremes.