Giving the position as the answer instead of the value
"The Position Problem"
The Mistake in Action
Find the median of 8 values where $\frac{n+1}{2} = 4.5$
Student writes: "The median is 4.5"
Why It Happens
Students correctly calculate the median position using $\frac{n+1}{2}$ but then give this position number as their answer, forgetting to actually look up what value is in that position.
The Fix
The formula $\frac{n+1}{2}$ tells you the position of the median, not the median itself!
For 8 ordered values, position = $\frac{8+1}{2} = 4.5$
This means: find the 4th and 5th values, then find their mean.
If the ordered data is: 2, 3, 5, 7, 8, 10, 12, 15
Median = $\frac{7+8}{2} = 7.5$
Spot the Mistake
Can you identify where this student went wrong?
8 values, so median position = (8+1) ÷ 2 = 4.5
Median = 4.5
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: