3 mistakes learners make with the median, each one named and explained.
The median is the middle of the ordered list, and ordering it first is not optional.
You add everything up and divide, and give that as the median.
Average is the word attached most firmly to adding up and dividing.
Question. 18, 11, 25, 14, 20, 9, 17
A common answer. 16.3, the mean
The answer. 17, the median
Why. Median means middle, and no adding is involved at all.
Three averages, three different methods. Read which one the question named.
You order the list correctly and then land one place either side of the middle.
Counting in from both ends at once is fiddly, and it is easy to stop a step early or late.
Question. 3, 4, 6, 7, 9
A common answer. 7, one place past the middle
The answer. 6
Why. Five values means the third one is the middle, with two either side.
Cross off one from each end at the same time until you meet. That never miscounts.
You take the middle number of the list as it was written, so 7, 3, 9, 4, 6 gives 9.
The question says middle, and the middle of the list on the page is right there.
Question. 7, 3, 9, 4, 6
A common answer. 9, the middle one as written
The answer. 6
Why. Ordered, the list is 3, 4, 6, 7, 9, and the middle of that is 6.
Order first, always. The median is the middle by size, not the middle by position.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.