Let’s carefully analyze the provided data for both types of tomatoes to determine which statement is true.
First, we look at the weights, the mean, and the mean absolute deviation (MAD) for each type of tomato.
### Plum Tomatoes
- Weights: 1, 1.2, 1.4, 2, 2.5 (ounces)
- Mean: 1.6 (ounces)
- Mean Absolute Deviation (MAD): 0.5 (ounces)
### Roma Tomatoes
- Weights: 2, 2, 3, 5, 5 (ounces)
- Mean: 3.4 (ounces)
- Mean Absolute Deviation (MAD): 1.3 (ounces)
### Analysis
1. Compare the Mean Absolute Deviations (MADs):
- Plum Tomatoes MAD: 0.5
- Roma Tomatoes MAD: 1.3
The mean absolute deviation measures the average distance between each data point and the mean. A smaller MAD indicates that the data points are closer to the mean.
Since the MAD for plum tomatoes (0.5) is less than that for Roma tomatoes (1.3), it implies that the weights of plum tomatoes are more clustered around the mean compared to Roma tomatoes.
Therefore, the statement weights of plum tomatoes are likely to be closer to the mean is true.
2. Compare the Maximum Weights:
- Maximum Weight of Plum Tomatoes: 2.5 (ounces)
- Maximum Weight of Roma Tomatoes: 5 (ounces)
The maximum weight of Roma tomatoes is greater than that of plum tomatoes.
3. Other Possible Statements:
- (B) Roma tomatoes always weigh more than plum tomatoes is false because not all Roma tomatoes weigh more than all plum tomatoes (for example, the smallest Roma tomatoes weigh 2 ounces, while some plum tomatoes weigh less and some more than 2 ounces).
- (D) Weights of Roma tomatoes are likely to be closer to the mean is false, as established earlier, because their MAD is larger than that of plum tomatoes.
### Conclusion
Based on the analysis, the correct and true statement is:
A. Weights of plum tomatoes are likely to be closer to the mean.
