6 mistakes learners make with range and spread, each one named and explained.
The range measures how spread out the data is. It is not an average and it is a subtraction.
The largest and smallest values are added together to give the range.
Combining two numbers usually means adding, and the range does use exactly those two.
Question. 12, 5, 9, 14, 7, 20
A common answer. 20 + 5 = 25
The answer. 20 - 5 = 15
Why. The range measures the gap between them, and a gap is a subtraction.
A range can never be larger than the largest value. That is the check.
The biggest number in the set is written down as the range.
The largest value is the most striking number and it is genuinely part of the calculation.
Question. 12, 5, 9, 14, 7, 20
A common answer. 20
The answer. 15
Why. 20 is where the data reaches, not how wide it is.
The range needs both ends. One number on its own can never be a spread.
The median is chosen as the average most affected by one very large value.
One extreme value clearly changes the data, so it feels like it should change every summary.
Question. 1, 2, 3, 4, 500
A common answer. the median is dragged upwards
The answer. the median stays at 3
Why. The median only cares about position, and moving one value to the far end does not move the middle.
The mean uses every value's size. The median uses only the order.
The mode is chosen as the average most affected by a single very large value.
Any change to the data looks like it should change the answer.
Question. Adding one value of 500 to a set
A common answer. the mode moves towards 500
The answer. the mode is unchanged unless 500 becomes the most common value
Why. A value that appears once cannot be the most frequent one.
An outlier is by definition unusual, so it is almost never the mode.
The answer given talks about the range when the question asked which average is affected.
The range is taught alongside the averages and is genuinely very sensitive to outliers.
Question. Which average is most affected by an outlier
A common answer. the range is not an average
The answer. the mean
Why. That statement is true, but the question asked which average, and the range is not one.
Check that a true statement is also an answer. Being correct is not enough.
Given the range and the lowest mark, the range is taken away instead of added on.
Range questions are subtractions, so subtracting is the habit even when working backwards.
Question. Range 18, lowest mark 27
A common answer. 27 - 18 = 9
The answer. 27 + 18 = 45
Why. The highest mark is above the lowest, so the range has to be added on.
Check the answer makes sense. A highest mark below the lowest one cannot be right.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.