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To answer the question and analyze the pumpkin weights from Cedartown and Baytown, we will follow these steps:
1. List the weights of pumpkins grown in Cedartown and Baytown.
- Cedartown pumpkin weights: 753, 575, 685.5, 718
- Baytown pumpkin weights: 622, 713.5, 579, 644
2. Calculate the average (mean) weight of the pumpkins from both towns.
To find the average weight:
- Sum the weights.
- Divide the sum by the number of weights.
For Cedartown:
- Sum of weights: [tex]\(753 + 575 + 685.5 + 718 = 2731.5\)[/tex]
- Number of weights: 4
- Average weight [tex]\(=\frac{2731.5}{4} = 682.875\)[/tex]
For Baytown:
- Sum of weights: [tex]\(622 + 713.5 + 579 + 644 = 2558.5\)[/tex]
- Number of weights: 4
- Average weight [tex]\(=\frac{2558.5}{4} = 639.625\)[/tex]
3. Calculate the Mean Absolute Deviation (MAD) for both towns.
The MAD is determined by:
- Calculating the absolute difference between each weight and the average weight.
- Summing these absolute differences.
- Dividing by the number of weights.
For Cedartown:
- Calculate absolute deviations from the average ([tex]\(682.875\)[/tex]):
- [tex]\(|753 - 682.875| = 70.125\)[/tex]
- [tex]\(|575 - 682.875| = 107.875\)[/tex]
- [tex]\(|685.5 - 682.875| = 2.625\)[/tex]
- [tex]\(|718 - 682.875| = 35.125\)[/tex]
- Sum of absolute deviations: [tex]\(70.125 + 107.875 + 2.625 + 35.125 = 215.75\)[/tex]
- MAD [tex]\(=\frac{215.75}{4} = 53.9375\)[/tex]
For Baytown:
- Calculate absolute deviations from the average ([tex]\(639.625\)[/tex]):
- [tex]\(|622 - 639.625| = 17.625\)[/tex]
- [tex]\(|713.5 - 639.625| = 73.875\)[/tex]
- [tex]\(|579 - 639.625| = 60.625\)[/tex]
- [tex]\(|644 - 639.625| = 4.375\)[/tex]
- Sum of absolute deviations: [tex]\(17.625 + 73.875 + 60.625 + 4.375 = 156.5\)[/tex]
- MAD [tex]\(=\frac{156.5}{4} = 39.125\)[/tex]
4. Summary of results:
- The average weight of pumpkins grown in Cedartown is [tex]\(682.875\)[/tex].
- The average weight of pumpkins grown in Baytown is [tex]\(639.625\)[/tex].
- The mean absolute deviation of the pumpkin weights in Cedartown is [tex]\(53.9375\)[/tex].
- The mean absolute deviation of the pumpkin weights in Baytown is [tex]\(39.125\)[/tex].
These are the detailed steps and results for calculating the average weights and mean absolute deviations for pumpkin weights from Cedartown and Baytown.
1. List the weights of pumpkins grown in Cedartown and Baytown.
- Cedartown pumpkin weights: 753, 575, 685.5, 718
- Baytown pumpkin weights: 622, 713.5, 579, 644
2. Calculate the average (mean) weight of the pumpkins from both towns.
To find the average weight:
- Sum the weights.
- Divide the sum by the number of weights.
For Cedartown:
- Sum of weights: [tex]\(753 + 575 + 685.5 + 718 = 2731.5\)[/tex]
- Number of weights: 4
- Average weight [tex]\(=\frac{2731.5}{4} = 682.875\)[/tex]
For Baytown:
- Sum of weights: [tex]\(622 + 713.5 + 579 + 644 = 2558.5\)[/tex]
- Number of weights: 4
- Average weight [tex]\(=\frac{2558.5}{4} = 639.625\)[/tex]
3. Calculate the Mean Absolute Deviation (MAD) for both towns.
The MAD is determined by:
- Calculating the absolute difference between each weight and the average weight.
- Summing these absolute differences.
- Dividing by the number of weights.
For Cedartown:
- Calculate absolute deviations from the average ([tex]\(682.875\)[/tex]):
- [tex]\(|753 - 682.875| = 70.125\)[/tex]
- [tex]\(|575 - 682.875| = 107.875\)[/tex]
- [tex]\(|685.5 - 682.875| = 2.625\)[/tex]
- [tex]\(|718 - 682.875| = 35.125\)[/tex]
- Sum of absolute deviations: [tex]\(70.125 + 107.875 + 2.625 + 35.125 = 215.75\)[/tex]
- MAD [tex]\(=\frac{215.75}{4} = 53.9375\)[/tex]
For Baytown:
- Calculate absolute deviations from the average ([tex]\(639.625\)[/tex]):
- [tex]\(|622 - 639.625| = 17.625\)[/tex]
- [tex]\(|713.5 - 639.625| = 73.875\)[/tex]
- [tex]\(|579 - 639.625| = 60.625\)[/tex]
- [tex]\(|644 - 639.625| = 4.375\)[/tex]
- Sum of absolute deviations: [tex]\(17.625 + 73.875 + 60.625 + 4.375 = 156.5\)[/tex]
- MAD [tex]\(=\frac{156.5}{4} = 39.125\)[/tex]
4. Summary of results:
- The average weight of pumpkins grown in Cedartown is [tex]\(682.875\)[/tex].
- The average weight of pumpkins grown in Baytown is [tex]\(639.625\)[/tex].
- The mean absolute deviation of the pumpkin weights in Cedartown is [tex]\(53.9375\)[/tex].
- The mean absolute deviation of the pumpkin weights in Baytown is [tex]\(39.125\)[/tex].
These are the detailed steps and results for calculating the average weights and mean absolute deviations for pumpkin weights from Cedartown and Baytown.
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