Which measures of center change when a value is deleted from these datasets?
Dataset 1: (0,1,0,1,3,2,0,1,0,1,0,2)
Dataset 2: (0,1,1,3,2,0,1,0,1,0,2)
(1 point)
Responses
Only the median changes.
Only the median changes.
Only the mean changes.
Only the mean changes.
Both the mean and median change.
Both the mean and median change.
Both the mode and mean change.
Both the mean and median change.
In Dataset 1: (0,1,0,1,3,2,0,1,0,1,0,2), if a value is deleted, the only measure of center that changes is the median. The median is the middle value when the data is arranged in ascending order. If a value is deleted, it may affect the position of the middle value, therefore changing the median.
In Dataset 2: (0,1,1,3,2,0,1,0,1,0,2), if a value is deleted, both the mean and median can change. The mean is calculated by summing up all the values and dividing by the number of values, so if a value is deleted, it will affect the total sum and hence change the mean. The median, as mentioned earlier, can also change if the deleted value affects the position of the middle value.
Therefore, the correct response is: Both the mean and median change.