Eric kept track of the low temperatures over a two-week period. His results are below.
Low Temperatures
Day Low Temperature (in °F)
1 73
2 68
3 72
4 77
5 81
6 73
7 78
8 72
9 82
10 76
11 82
12 86
13 81
14 77
What is the mean absolute deviation of the temperatures?
A.
2
B.
52
C.
4
D.
77
To find the mean absolute deviation (MAD) of the temperatures, we first need to find the mean temperature.
The mean temperature is the sum of all the temperatures divided by the number of temperatures.
Sum of temperatures = 73 + 68 + 72 + 77 + 81 + 73 + 78 + 72 + 82 + 76 + 82 + 86 + 81 + 77 = 1040
Number of temperatures = 14
Mean temperature = 1040/14 = 74.29 (rounded to two decimal places)
Next, we need to find the absolute deviation of each temperature from the mean.
Absolute deviation = |Temperature - Mean temperature|
Absolute deviations:
|73 - 74.29| = 1.29
|68 - 74.29| = 6.29
|72 - 74.29| = 2.29
|77 - 74.29| = 2.71
|81 - 74.29| = 6.71
|73 - 74.29| = 1.29
|78 - 74.29| = 3.71
|72 - 74.29| = 2.29
|82 - 74.29| = 7.71
|76 - 74.29| = 1.71
|82 - 74.29| = 7.71
|86 - 74.29| = 11.71
|81 - 74.29| = 6.71
|77 - 74.29| = 2.71
Now, we find the mean of the absolute deviations.
Sum of absolute deviations = 1.29 + 6.29 + 2.29 + 2.71 + 6.71 + 1.29 + 3.71 + 2.29 + 7.71 + 1.71 + 7.71 + 11.71 + 6.71 + 2.71 = 64.29
MAD = Sum of absolute deviations / Number of temperatures = 64.29 / 14 ≈ 4.59 (rounded to two decimal places)
Therefore, the mean absolute deviation of the temperatures is approximately 4.59.
The closest option is C. 4.