During a week in Santa Fe, the following temperatures are recorded in degrees Fahrenheit: 75, 83, 77, 61, 82, 67, and 45. What is the mean absolute deviation of this set of temperatures?

• 13.2
• 7.5
• 10.6
• 6.7

10.6 Correct

Thank you!

To find the mean absolute deviation (MAD) of a set of numbers, you need to follow these steps:

1. Find the mean (average) of the temperatures by adding up all the numbers and dividing by the total number of temperatures.

To find the mean, add up all the temperatures:
75 + 83 + 77 + 61 + 82 + 67 + 45 = 490

Divide the sum by the number of temperatures:
490 / 7 = 70

2. Find the absolute deviation for each temperature. Absolute deviation is the absolute value of the difference between each temperature and the mean.

Absolute deviation for the first temperature (75 - 70 = 5)
Absolute deviation for the second temperature (83 - 70 = 13)
Absolute deviation for the third temperature (77 - 70 = 7)
Absolute deviation for the fourth temperature (61 - 70 = 9)
Absolute deviation for the fifth temperature (82 - 70 = 12)
Absolute deviation for the sixth temperature (67 - 70 = 3)
Absolute deviation for the seventh temperature (45 - 70 = 25)

3. Find the mean of the absolute deviations. Add up the absolute deviations and divide by the total number of temperatures.

Mean of the absolute deviations:
(5 + 13 + 7 + 9 + 12 + 3 + 25) / 7 = 10.6

Therefore, the mean absolute deviation of this set of temperatures is 10.6.

The correct answer is:
• 10.6