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.
