If we change the value of 71° to 93°, then the new list becomes:
58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57
To find out which of the measures changes the most, we need to calculate the values before and after the change.
Before the change:
- Mean = (58+61+71+77+91+100+105+102+95+82+66+57)/12 = 82.3°
- Median = 84° (the middle value after sorting the list in ascending order)
- Range = 105° - 57° = 48°
- IQR = Q3 - Q1 = 100° - 61° = 39°
After the change:
- Mean = (58+61+93+77+91+100+105+102+95+82+66+57)/12 = 83.8°
- Median = 86.5° (the middle value after sorting the list in ascending order)
- Range = 105° - 57° = 48°
- IQR = Q3 - Q1 = 100° - 61° = 39°
Therefore, the measures that remain unchanged are range and IQR. The measures that change the most are mean and median. The new value of the mean is 83.8°. So the answer is A: Mean 82.3° changes to 83.8°.