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Sagot :
To determine the statistical measures for the weights of pumpkins grown in Cedartown and Baytown, let's break down the tasks and calculate each required value step-by-step.
### Cedartown Pumpkins
First, we will find the average weight of the Cedartown pumpkins.
Step 1: List the weights of the Cedartown pumpkins:
[tex]\[ 611, 753, 575, 685.5, 718 \][/tex]
Step 2: Calculate the average (mean) weight:
[tex]\[ \text{Mean} = \frac{611 + 753 + 575 + 685.5 + 718}{5} \][/tex]
[tex]\[ \text{Mean} = 668.5 \][/tex]
### Baytown Pumpkins
Next, we will find the average weight of the Baytown pumpkins.
Step 1: List the weights of the Baytown pumpkins:
[tex]\[ 584, 622, 713.5, 579, 644 \][/tex]
Step 2: Calculate the average (mean) weight:
[tex]\[ \text{Mean} = \frac{584 + 622 + 713.5 + 579 + 644}{5} \][/tex]
[tex]\[ \text{Mean} = 628.5 \][/tex]
### Mean Absolute Deviation (MAD)
The Mean Absolute Deviation (MAD) gives us an idea of how much the weights of the pumpkins deviate from the average weight.
#### Cedartown Pumpkins MAD
Step 1: Calculate the absolute deviations from the mean for each pumpkin:
[tex]\[ |611 - 668.5| = 57.5 \][/tex]
[tex]\[ |753 - 668.5| = 84.5 \][/tex]
[tex]\[ |575 - 668.5| = 93.5 \][/tex]
[tex]\[ |685.5 - 668.5| = 17 \][/tex]
[tex]\[ |718 - 668.5| = 49.5 \][/tex]
Step 2: Calculate the mean of these absolute deviations:
[tex]\[ \text{MAD} = \frac{57.5 + 84.5 + 93.5 + 17 + 49.5}{5} \][/tex]
[tex]\[ \text{MAD} = 60.4 \][/tex]
#### Baytown Pumpkins MAD
Step 1: Calculate the absolute deviations from the mean for each pumpkin:
[tex]\[ |584 - 628.5| = 44.5 \][/tex]
[tex]\[ |622 - 628.5| = 6.5 \][/tex]
[tex]\[ |713.5 - 628.5| = 85 \][/tex]
[tex]\[ |579 - 628.5| = 49.5 \][/tex]
[tex]\[ |644 - 628.5| = 15.5 \][/tex]
Step 2: Calculate the mean of these absolute deviations:
[tex]\[ \text{MAD} = \frac{44.5 + 6.5 + 85 + 49.5 + 15.5}{5} \][/tex]
[tex]\[ \text{MAD} = 40.2 \][/tex]
### Summary
- The average weight of pumpkins grown in Cedartown: 668.5 pounds
- The mean absolute deviation of the pumpkin weights in Cedartown: 60.4 pounds
- The average weight of pumpkins grown in Baytown: 628.5 pounds
- The mean absolute deviation of the pumpkin weights in Baytown: 40.2 pounds
These steps establish that the given data has been accurately analyzed to provide the mean and mean absolute deviation for pumpkin weights in both Cedartown and Baytown.
### Cedartown Pumpkins
First, we will find the average weight of the Cedartown pumpkins.
Step 1: List the weights of the Cedartown pumpkins:
[tex]\[ 611, 753, 575, 685.5, 718 \][/tex]
Step 2: Calculate the average (mean) weight:
[tex]\[ \text{Mean} = \frac{611 + 753 + 575 + 685.5 + 718}{5} \][/tex]
[tex]\[ \text{Mean} = 668.5 \][/tex]
### Baytown Pumpkins
Next, we will find the average weight of the Baytown pumpkins.
Step 1: List the weights of the Baytown pumpkins:
[tex]\[ 584, 622, 713.5, 579, 644 \][/tex]
Step 2: Calculate the average (mean) weight:
[tex]\[ \text{Mean} = \frac{584 + 622 + 713.5 + 579 + 644}{5} \][/tex]
[tex]\[ \text{Mean} = 628.5 \][/tex]
### Mean Absolute Deviation (MAD)
The Mean Absolute Deviation (MAD) gives us an idea of how much the weights of the pumpkins deviate from the average weight.
#### Cedartown Pumpkins MAD
Step 1: Calculate the absolute deviations from the mean for each pumpkin:
[tex]\[ |611 - 668.5| = 57.5 \][/tex]
[tex]\[ |753 - 668.5| = 84.5 \][/tex]
[tex]\[ |575 - 668.5| = 93.5 \][/tex]
[tex]\[ |685.5 - 668.5| = 17 \][/tex]
[tex]\[ |718 - 668.5| = 49.5 \][/tex]
Step 2: Calculate the mean of these absolute deviations:
[tex]\[ \text{MAD} = \frac{57.5 + 84.5 + 93.5 + 17 + 49.5}{5} \][/tex]
[tex]\[ \text{MAD} = 60.4 \][/tex]
#### Baytown Pumpkins MAD
Step 1: Calculate the absolute deviations from the mean for each pumpkin:
[tex]\[ |584 - 628.5| = 44.5 \][/tex]
[tex]\[ |622 - 628.5| = 6.5 \][/tex]
[tex]\[ |713.5 - 628.5| = 85 \][/tex]
[tex]\[ |579 - 628.5| = 49.5 \][/tex]
[tex]\[ |644 - 628.5| = 15.5 \][/tex]
Step 2: Calculate the mean of these absolute deviations:
[tex]\[ \text{MAD} = \frac{44.5 + 6.5 + 85 + 49.5 + 15.5}{5} \][/tex]
[tex]\[ \text{MAD} = 40.2 \][/tex]
### Summary
- The average weight of pumpkins grown in Cedartown: 668.5 pounds
- The mean absolute deviation of the pumpkin weights in Cedartown: 60.4 pounds
- The average weight of pumpkins grown in Baytown: 628.5 pounds
- The mean absolute deviation of the pumpkin weights in Baytown: 40.2 pounds
These steps establish that the given data has been accurately analyzed to provide the mean and mean absolute deviation for pumpkin weights in both Cedartown and Baytown.
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