A local weather station collected the 12 p.m. temperature at 5 different locations in its town:

Question

Temperatures, °F: {63, 59, 60, 61, 62}

What is the estimated mean absolute deviation of the 12 p.m. temperatures in the town?



Responses

1.2°F
1.2°F

1.4°F
1.4°F

6°F
6°F

61°F

Answer 1

To calculate the mean absolute deviation (MAD) of the temperatures, follow these steps:

1. Calculate the Mean: First, find the mean (average) of the temperatures. \[ \text{Mean} = \frac{(63 + 59 + 60 + 61 + 62)}{5} = \frac{305}{5} = 61°F \]

2. Calculate the Absolute Deviations: Next, find the absolute deviations from the mean:

   • For 63°F: \( |63 - 61| = 2 \)
   • For 59°F: \( |59 - 61| = 2 \)
   • For 60°F: \( |60 - 61| = 1 \)
   • For 61°F: \( |61 - 61| = 0 \)
   • For 62°F: \( |62 - 61| = 1 \)

   Thus, the absolute deviations are: \(2, 2, 1, 0, 1\).

3. Calculate the Mean Absolute Deviation: Now, calculate the mean of these absolute deviations: \[ \text{MAD} = \frac{(2 + 2 + 1 + 0 + 1)}{5} = \frac{6}{5} = 1.2°F \]

Thus, the estimated mean absolute deviation of the 12 p.m. temperatures in the town is 1.2°F.