Maths

Common mistakes in the median

3 mistakes learners make with the median, each one named and explained.

All common mistakes

The median is the middle of the ordered list, and ordering it first is not optional.

The mean given where the median was asked for

What it looks like

You add everything up and divide, and give that as the median.

Why it happens

Average is the word attached most firmly to adding up and dividing.

A worked example

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.

Put the two side by side

Mean: add and divide.
Median: order and pick the middle.

Three averages, three different methods. Read which one the question named.

The middle position counted wrongly

What it looks like

You order the list correctly and then land one place either side of the middle.

Why it happens

Counting in from both ends at once is fiddly, and it is easy to stop a step early or late.

A worked example

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.

Put the two side by side

Five values: the middle is the third.
Six values: there is no single middle, so take the mean of the third and fourth.

Cross off one from each end at the same time until you meet. That never miscounts.

The middle taken without ordering first

What it looks like

You take the middle number of the list as it was written, so 7, 3, 9, 4, 6 gives 9.

Why it happens

The question says middle, and the middle of the list on the page is right there.

A worked example

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.

Put the two side by side

Middle of the list as printed: 9.
Middle of the ordered list: 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.

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