Question

THE AVERAGE HIGH OF TEMPERATURES IN DEGREES FOR A CITY ARE LISTEED.

58, 61, 71, 77, 99, 100, 105, 102, 95, 82, 66, 57.
if a value of 120.5 degrees is added, how does the mean change and by how much?

A. the mean stays at 83.5
B. the mean increases by 3.5
C. The mean increases by 3.1
D. The mean stays at 80.4


WORTH 20 POINTS

Answer 1

To find the mean, you need to add up all the temperatures and then divide by the number of temperatures. Let's first calculate the mean without the value of 120.5 degrees:

Sum of temperatures (without 120.5): 58 + 61 + 71 + 77 + 99 + 100 + 105 + 102 + 95 + 82 + 66 + 57 = 973
Number of temperatures (without 120.5): 12

Mean (without 120.5) = Sum of temperatures / Number of temperatures = 973 / 12 ≈ 81.08

Now, let's include the value of 120.5 degrees and recalculate the mean:

Sum of temperatures (with 120.5): 973 + 120.5 = 1093.5
Number of temperatures (with 120.5): 12 + 1 = 13

Mean (with 120.5) = Sum of temperatures / Number of temperatures = 1093.5 / 13 ≈ 84.12

Now, let's find out how much the mean changed:

Mean with the value of 120.5 degrees ≈ 84.12
Mean without the value of 120.5 degrees ≈ 81.08

Change in mean ≈ Mean with value - Mean without value
Change in mean ≈ 84.12 - 81.08 ≈ 3.04

Therefore, the mean increases by approximately 3.04 degrees when the value of 120.5 degrees is added.

The closest answer to this change is:

C. The mean increases by 3.1