Question
If the mean birth weight is grams, which of the following statements is true?
Responses
A The median birth weight can not be determined from the information givenThe median birth weight can not be determined from the information given
B The mean birth weight is the same as the median birth weightThe mean birth weight is the same as the median birth weight
C The mean birth weight is larger than the median birth weightThe mean birth weight is larger than the median birth weight
D The median birth weight is larger than the mean birth weight
Responses
A The median birth weight can not be determined from the information givenThe median birth weight can not be determined from the information given
B The mean birth weight is the same as the median birth weightThe mean birth weight is the same as the median birth weight
C The mean birth weight is larger than the median birth weightThe mean birth weight is larger than the median birth weight
D The median birth weight is larger than the mean birth weight
Answers
GPT-4o mini
To determine which statement is true regarding the relationship between the mean and median birth weights, we need to consider the characteristics of the distribution of birth weights.
1. **If the distribution is symmetric** (like a normal distribution), the mean and median are equal (A: false, B: true).
2. **If the distribution is skewed right** (where a few high values pull the mean higher), the mean will be larger than the median (C: true, D: false).
3. **If the distribution is skewed left** (where a few low values pull the mean lower), the mean will be smaller than the median (C: false, D: true).
Without additional information about the shape of the distribution of birth weights, we cannot definitively conclude which statement is true. Therefore:
- **A** is correct that we cannot determine the median from the given information unless we know more about the distribution.
So the best answer to choose here is **A: The median birth weight cannot be determined from the information given**.
1. **If the distribution is symmetric** (like a normal distribution), the mean and median are equal (A: false, B: true).
2. **If the distribution is skewed right** (where a few high values pull the mean higher), the mean will be larger than the median (C: true, D: false).
3. **If the distribution is skewed left** (where a few low values pull the mean lower), the mean will be smaller than the median (C: false, D: true).
Without additional information about the shape of the distribution of birth weights, we cannot definitively conclude which statement is true. Therefore:
- **A** is correct that we cannot determine the median from the given information unless we know more about the distribution.
So the best answer to choose here is **A: The median birth weight cannot be determined from the information given**.