Answer:
(a) Median, 86.5
Explanation:
You want to know which measure changes the most, and its new value, when 58 is changed to 101 in the given list.
Old values
The sorted list is ...
{57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105}
The median is the average of the 6th and 7th values: (77+82)/2 = 79.5.
The mean is the sum divided by 12, about 80.4.
The range is the difference of highest and lowest: 105-57 = 48.
The IQR is the difference between the average of the 9th and 10th numbers and the average of the 3rd and 4th numbers:
(95+100)/2 -(61+66)/2 = 34
New values
The sorted list after the change of values is ...
{57, 61, 66, 71, 77, 82, 91, 95, 100, 101, 102, 105}
The median is (82+91)/2 = 86.5, a change of 86.5 -79.5 = 7.
The mean is 84, a change of about 3.6.
The range is the same at 48, a change of 0.
The IQR is (100+101)/2 -(66 +71)/2 = 32, a change of -2.
The measure that changed the most is the median, which has a new value of 86.5, matching choice A.
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