Answer: Median
Explanation:
To determine which value would change the most if the number 71 replaced one of the 81's in the set, we can calculate the mean, median, and mode of the original set of numbers and the modified set where one of the 81's is replaced with 71.
Original set: 82 81 81 80 71
Modified set: 82 81 71 80 71
Mean:
The mean is the average of the numbers in the set. To calculate the mean, we add up all the numbers in the set and divide by the total number of numbers:
Mean of original set: (82 + 81 + 81 + 80 + 71) / 5 = 79
Mean of modified set: (82 + 81 + 71 + 80 + 71) / 5 = 77
The mean of the modified set is lower than the mean of the original set, indicating that replacing one of the 81's with 71 reduces the mean.
Median:
The median is the middle value when the numbers are arranged in order. To calculate the median, we first need to put the numbers in order:
Original set: 71 80 81 81 82
Modified set: 71 71 80 81 82
Median of original set: 81
Median of modified set: 80
The median of the modified set is lower than the median of the original set, indicating that replacing one of the 81's with 71 reduces the median.
Mode:
The mode is the value that appears most frequently in the set. If there is more than one value that appears most frequently, then the set is said to have multiple modes. To calculate the mode, we need to count how many times each value appears in the set:
Original set: 82 81 81 80 71
Modified set: 82 81 71 80 71
Mode of original set: 81
Mode of modified set: 71
The mode of the original set is 81 because it appears twice, which is more than any other value. The mode of the modified set is 71 because it appears twice, which is more than any other value. So the mode does not change when one of the 81's is replaced with 71.
Therefore, we can conclude that the median would change the most if the number 71 replaced one of the 81's in the set.