Question

The median and range of 15 measurements are 18 and 5, respectively. If 3 is subtracted from each of the 15 measurements, which of the following statements regarding the median and range of the modified 15 measurements must be true?

1) The median and range will both decrease.
2) The median and range will both stay the same.
3) The median will stay the same, but the range will decrease.
4) The median will stay the same, but the range will increase.
5) The median will decrease, but the range will stay the same.

Answer 1

When a constant is subtracted from each measurement in a data set, the median decreases by that constant, but the range remains unchanged.

Step-by-step explanation:

The question deals with the effect on the median and range when a constant number is subtracted from every measurement in a data set. Subtracting a constant from each measurement will decrease the value of each measurement by that amount, but it does not change the spacing between the measurements. Therefore, the median will decrease by the same constant because it is the middle value, and the range will stay the same because it is the difference between the highest and lowest values, which both decrease by the constant but maintain their relative distance from each other.

So, the answer to the student's question is: The median will decrease, but the range will stay the same.