Given the weights of pumpkins grown in Cedartown and Baytown, we are asked to compute the following:
1. The average weight of pumpkins in Cedartown.
2. The average weight of pumpkins in Baytown.
3. The Mean Absolute Deviation (MAD) of pumpkin weights in Cedartown.
4. The Mean Absolute Deviation (MAD) of pumpkin weights in Baytown.
Let's start with step-by-step calculations:
### 1. Average Weight of Pumpkins in Cedartown
The weights of Cedartown pumpkins are: 611, 753, 575, 685.5, 718
To find the average weight:
- Sum the weights: [tex]\( 611 + 753 + 575 + 685.5 + 718 = 3342.5 \)[/tex]
- Divide by the number of weights (5):
[tex]\[
\text{Average} = \frac{3342.5}{5} = 668.5
\][/tex]
So, the average weight of pumpkins in Cedartown is 668.5 pounds.
### 2. Average Weight of Pumpkins in Baytown
The weights of Baytown pumpkins are: 584, 622, 713.5, 579, 644
To find the average weight:
- Sum the weights: [tex]\( 584 + 622 + 713.5 + 579 + 644 = 3142.5 \)[/tex]
- Divide by the number of weights (5):
[tex]\[
\text{Average} = \frac{3142.5}{5} = 628.5
\][/tex]
So, the average weight of pumpkins in Baytown is 628.5 pounds.
### 3. Mean Absolute Deviation (MAD) of Pumpkin Weights in Cedartown
To compute the MAD, we need to follow these steps:
- Calculate the absolute deviations from the average weight.
- The absolute deviations are: [tex]\(|611 - 668.5|, |753 - 668.5|, |575 - 668.5|, |685.5 - 668.5|, |718 - 668.5|\)[/tex]
- Numerically they are: [tex]\(57.5, 84.5, 93.5, 17, 49.5\)[/tex]
- Sum of absolute deviations: [tex]\(57.5 + 84.5 + 93.5 + 17 + 49.5 = 302\)[/tex]
- Divide by the number of weights (5):
[tex]\[
\text{MAD} = \frac{302}{5} = 60.4
\][/tex]
So, the Mean Absolute Deviation of pumpkin weights in Cedartown is 60.4 pounds.
### 4. Mean Absolute Deviation (MAD) of Pumpkin Weights in Baytown
To compute the MAD, we need to follow these steps:
- Calculate the absolute deviations from the average weight.
- The absolute deviations are: [tex]\(|584 - 628.5|, |622 - 628.5|, |713.5 - 628.5|, |579 - 628.5|, |644 - 628.5|\)[/tex]
- Numerically they are: [tex]\(44.5, 6.5, 85, 49.5, 15.5\)[/tex]
- Sum of absolute deviations: [tex]\(44.5 + 6.5 + 85 + 49.5 + 15.5 = 201\)[/tex]
- Divide by the number of weights (5):
[tex]\[
\text{MAD} = \frac{201}{5} = 40.2
\][/tex]
So, the Mean Absolute Deviation of pumpkin weights in Baytown is 40.2 pounds.
