Answer:
The mean increases by 3.5°.
Explanation:
To determine how the mean changes when a value of 120.5° is added to the data, we need to recalculate the mean before and after the addition.
Given the average high temperatures:
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
To find the original mean, we sum up all the temperatures and divide by the number of data points:
(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 904 / 12 = 75.33°
Now, let's add the value of 120.5° to the data:
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 120.5
To find the new mean, we sum up all the temperatures (including the added value) and divide by the number of data points:
(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 120.5) / 13 = 1025.5 / 13 ≈ 78.88°
The mean has increased from 75.33° to 78.88°.
Therefore, the mean increases by approximately 3.55° (rounded to the nearest tenth).
The correct answer is: The mean increases by 3.5°.