Let's break down the solution step-by-step for the given problem, using the weights of the pumpkins from Cedartown and Baytown.
### Step 1: Calculate the Average Weight
#### Cedartown Pumpkins
The weights of the Cedartown pumpkins are:
611, 753, 575, 685.5, 718
To find the average weight of Cedartown pumpkins, we sum these weights and divide by the number of pumpkins.
[tex]\[
\text{Average weight of Cedartown pumpkins} = \frac{611 + 753 + 575 + 685.5 + 718}{5} = 668.5 \text{ pounds}
\][/tex]
#### Baytown Pumpkins
The weights of the Baytown pumpkins are:
584, 622, 713.5, 579, 644
Similarly, to find the average weight of Baytown pumpkins, we sum these weights and divide by the number of pumpkins.
[tex]\[
\text{Average weight of Baytown pumpkins} = \frac{584 + 622 + 713.5 + 579 + 644}{5} = 628.5 \text{ pounds}
\][/tex]
### Step 2: Calculate the Mean Absolute Deviation (MAD)
#### Cedartown Pumpkins MAD
First, we calculate the absolute deviations from the average:
[tex]\[
\begin{align*}
|611 - 668.5| &= 57.5 \\
|753 - 668.5| &= 84.5 \\
|575 - 668.5| &= 93.5 \\
|685.5 - 668.5| &= 17.0 \\
|718 - 668.5| &= 49.5 \\
\end{align*}
\][/tex]
Next, we find the average of these absolute deviations:
[tex]\[
\text{MAD of Cedartown pumpkins} = \frac{57.5 + 84.5 + 93.5 + 17.0 + 49.5}{5} = 60.4
\][/tex]
#### Baytown Pumpkins MAD
For the Baytown pumpkins, calculate the absolute deviations from the average:
[tex]\[
\begin{align*}
|584 - 628.5| &= 44.5 \\
|622 - 628.5| &= 6.5 \\
|713.5 - 628.5| &= 85.0 \\
|579 - 628.5| &= 49.5 \\
|644 - 628.5| &= 15.5 \\
\end{align*}
\][/tex]
Next, we find the average of these absolute deviations:
[tex]\[
\text{MAD of Baytown pumpkins} = \frac{44.5 + 6.5 + 85.0 + 49.5 + 15.5}{5} = 40.2
\][/tex]
### Final Results
Based on the calculations:
- The average weight of pumpkins grown in Cedartown is [tex]\(668.5 \text{ pounds}\)[/tex].
- The average weight of pumpkins grown in Baytown is [tex]\(628.5 \text{ pounds}\)[/tex].
- The mean absolute deviation of the pumpkin weights in Cedartown is [tex]\(60.4\)[/tex].
- The mean absolute deviation of the pumpkin weights in Baytown is [tex]\(40.2\)[/tex].
