The Mathematical Ninja gets mean

Chair: If 'good' requires pupil performance to exceed the national average, and if all schools must be good, how is this, how is this mathematically possible?

Michael Gove: By getting better all the time.

Chair: So it is possible, is it?

Michael Gove: It is possible to get better all the time.

- Oral evidence taken before the Education Committee, January 2012 (HC 1786-i, Q98-99)

The Mathematical Ninja sharpened his assegai. This was going to be a long class, assuming the student survived the first few questions.

He started with an easy one. "Can every football team finish top of the league?"

The student shook his ridiculous, puffy-cheeked head. "No, that would be ridiculous."

"Can every football team finish in the top half of the table?"

The shaking continued. "No, half of the teams end up in the top half and half in the bottom."

"Correct," said the Mathematical Ninja. "Can all of the teams have more than the median number of points?"

The student thought for a moment. "No," he said, after a pause. "Although, if more than half of the teams have the same score, and it's the worst score in the league, everyone could have at least the median number of points."

The Mathematical Ninja nodded, but decided against putting down his weapon. "How about the mode? Can every team exceed the mode?"

"Again, no," said the student. "By definition, at least two of the teams have the modal number of points. If the mode is also the minimum, though, everyone could have at least the modal number of points."

"OK," said the Mathematical Ninja, patiently. "How about the mean? Could every team exceed, let's say, the mean number of goals scored?"

The student didn't even blink. "As long as they keep getting better, yes."

The Mathematical Ninja did blink. He blinked long and hard. His weapon hand trembled. "I beg your pardon?"

"As long as they keep improving, everyone can be better than average."

It took all of the Mathematical Ninja's calmness training to leave the student's head attached to his shoulders. "You know, the Secretary of State is proposing that this sort of average calculation become mandatory for anyone training to be a teacher?"

The student nodded, merrily. "It would be outrageous for someone who didn't grasp averages to be in a position of responsibility over students, wouldn't it?"

"Wouldn't it just," said the Mathematical Ninja. "Wouldn't it just."

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

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