Median vs Percentile
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Median
Describing data
The median is the middle value of an ordered data set, splitting it so that half the values fall below and half above.
To find the median you sort the data and take the center value, averaging the two middle values when the count is even. For example, for 3, 7, and 10 the median is 7, while for 2, 6, 8, and 10 it is . Because it depends only on position, not on the size of extreme values, the median resists outliers. This makes the median a better center than the mean for strongly skewed data.
Percentile
Describing data
A percentile is a value at or below which a given percentage of the data falls, so about 90 percent of values lie at or below the 90th percentile.
The kth percentile is the value at or below which about percent of the observations lie. For example, if your test score is at the 85th percentile, roughly 85 percent of test-takers scored at or below you. Quartiles are percentiles too: the first quartile is the 25th percentile and the median is the 50th. Percentiles let you compare a single value to a whole distribution without knowing its shape.