Midrange vs Median

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.

Midrange

Describing data

The midrange is the average of the smallest and largest values in a data set, a quick measure of center that a single outlier can drag around.

The midrange uses only the two most extreme observations, so it is fast to compute and easy to distort. You find it with midrange=min+max2\text{midrange} = \frac{\min + \max}{2}. For a week of high temperatures whose smallest value is 41 degrees and largest is 77 degrees, the midrange is (41+77)/2=59(41 + 77)/2 = 59 degrees. Because everything between the extremes is ignored, one unusually large value moves the midrange much more than it moves the mean or the median.

Full entry for midrange

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 (6+8)/2=7(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.

Full entry for median

Where each one fits in the course