Question

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


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**.