Final answer:
Subtracting the same amount from each value in a data set decreases the mean, median, and mode by that amount but does not change the range, since every data point is adjusted equally. The relative positions of the mean, median, and mode remain constant unless the subtraction changes the data ordering.
Step-by-step explanation:
Subtracting the same amount from each value in a data set affects the measures of central tendency and the range in the following ways:
- The mean (or average) of the data set will decrease by the same amount that was subtracted from each value, as the mean is the sum of all the data values divided by the number of values.
- The median, or the middle value of the ordered data set, will also decrease by the amount subtracted because the position of the median does not change, only its value does.
- The mode, or the most frequently occurring value in the data set, decreases by the same amount if the data set has a mode. It remains the most frequent value but its actual number is reduced.
- The range, which is the difference between the largest and smallest values in the data set, remains unchanged because the same amount is subtracted from both extremes, thus not affecting the distance between them.