7 mistakes learners make with the mean, each one named and explained.
The mean shares the total out equally, so it needs the total and the count, every time.
A value of zero is skipped when counting how many items there are, so the mean comes out high.
Zero contributes nothing to the total, so it looks as though it contributes nothing at all.
Question. 2, 0, 3, 1, 4, 2
A common answer. 12 / 5 = 2.4
The answer. 12 / 6 = 2
Why. The zero is still a match that was played, so it still counts as one of the six.
Count the items, not the non-zero items. A zero is data.
The weighting is applied the wrong way round, so 6 at 70 and 4 at 80 comes out as 76.
Four numbers in one sentence, and which size belongs to which mean is easy to cross over.
Question. 6 pupils averaging 70 and 4 averaging 80
A common answer. (4 x 70 + 6 x 80) / 10 = 76
The answer. 74
Why. The larger group is the one averaging 70, so the answer sits below the midpoint of 75.
Check which side of the midpoint your answer lands on. The bigger group has to win.
A new value is added to a set and the mean is given as it was before.
One extra value among several feels too small to shift anything.
Question. Five pupils averaging 150 cm, joined by one of 162 cm
A common answer. the mean is still 150 cm
The answer. the mean is 152 cm
Why. The new pupil is above the old mean, so the mean has to rise.
Compare the new value with the old mean. That tells you the direction before any arithmetic.
A missing value is guessed from the other values rather than worked back from the total.
Working backwards feels like a different kind of problem from working the mean out forwards.
Question. Mean of five numbers is 12; four of them are 8, 15, 10 and 11
A common answer. 11, from the pattern of the others
The answer. 16
Why. Five numbers with a mean of 12 must total 60, and the four given total 44.
Mean times count always gives the total. That single step turns any of these round.
The values are added up correctly and the total is written down as the answer.
Adding is the visible work, and dividing is one small step that is easy to skip.
Question. 2, 0, 3, 1, 4, 2 over six matches
A common answer. 12
The answer. 2
Why. 12 is the goals scored altogether, not the goals per match.
A mean is always smaller than the total. If yours is not, the division is missing.
You correctly find the total but then give it, or the four values' total, as the answer.
Reaching the total feels like arriving, because it was the hard step.
Question. Mean of five is 12; four are 8, 15, 10 and 11
A common answer. 44
The answer. 60 - 44 = 16
Why. 44 is the four values you already had, not the one you were looking for.
The missing value is always a difference between those two totals.
Two group means are added and halved, so 70 for six pupils and 80 for four gives 75.
Averaging two numbers is the obvious move, and the group sizes look like background detail.
Question. 6 pupils averaging 70 and 4 averaging 80
A common answer. (70 + 80) / 2 = 75
The answer. 74
Why. More pupils sat in the group averaging 70, so the answer must be pulled towards 70.
Whenever the groups differ in size, go back to totals: total score over total people.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.