Final answer:
After adding a value of 98° to the data, the mean temperature increases by approximately 1.93°, which was not one of the provided options. The original mean was 72.92°, and the new mean with the added value is 74.85°.
Step-by-step explanation:
To determine how the mean changes when a new value is added to a data set, you must first calculate the original mean and then calculate the new mean after adding the new value. The original data has 12 values: 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57. The total sum of these values is 875. The mean, therefore, is 875 divided by 12, which equals approximately 72.92°.
With the new temperature added, 98°, the new sum is 875 + 98, which equals 973. Now the new mean is 973 divided by the 13 values, which equals approximately 74.85°.
Comparing the original mean to the new mean after adding 98° shows an increase. 74.85° - 72.92° equals approximately 1.93°. Thus, the mean increases by 1.93°, not any of the other provided options.