Median vs Quartile

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 $(6 + 8) / 2 = 7$. 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.

Quartiles split ordered data into four parts, marked by the first quartile $Q_1$, the median, and the third quartile $Q_3$. The first quartile is the median of the lower half and the third quartile is the median of the upper half. For example, in 2, 4, 6, 8, 10 the median is 6, so you exclude it and get $Q_1 = 3$ and $Q_3 = 9$. This site uses the median-excluded convention (the TI-84 method), which drops the overall median when the count is odd.