Lessons · Teaching · mean, median, and the average that hides two groups
The mean, the median, and the average that hides two groups
The mean is the total divided by the count and the median is the middle value once the scores are in order; when a class splits into two groups, the mean describes nobody in the room.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
Your class average is 62 and the meeting moves on. In the room there are eleven people on about 40 and nineteen on about 75, and there is nobody at all on 62. Any lesson planned for the average is planned for a person who does not exist.
How to think about it
Never accept a mean on its own. Put the scores in order, take the middle one, and look at the shape: how many under 50, how many over 80. Three numbers take two minutes and change what you plan.
Worked example
Five scores in order: 30, 40, 70, 75, 85In order first. A median out of order is meaningless.
Mean = (30 + 40 + 70 + 75 + 85) / 5 = 60Total over count.
Median = 70The middle one, with two above and two below.
Mean 60, median 70, and nobody near 60The gap between the two is the signal that the class is in two groups.
Your turn
Five scores in order are 20, 30, 55, 80 and 90. Write the line that gives the median.
20, 30, 55, 80, 90: median =
Solve one, graded on the server
The trap
Reporting the mean because that is the column the spreadsheet made. The spreadsheet does not know your class is in two groups; the ordered list does, and reading it takes two minutes.