Is the mean or median a better representation of the data set of the weights of a dog and her newborn puppies? Explain your reasoning.

To determine whether the mean or median is a better representation of the data set of the weights of a dog and her newborn puppies, we need to consider the characteristics of the data and the definitions of mean and median. 1. **Mean**: The mean is calculated by adding all the values together and dividing by the number of values. It is sensitive to extreme values (outliers). For example, if one of the puppies is significantly heavier or lighter than the others, it can skew the mean. 2. **Median**: The median is the middle value when the data set is ordered from least to greatest. It is less affected by outliers and provides a better measure of central tendency when the data is skewed or contains extreme values. ### Reasoning: - **Presence of Outliers**: In the case of weights of a dog and her newborn puppies, there is likely to be a significant difference in weight between the adult dog and the puppies. This difference can create an outlier effect, where the mean is disproportionately influenced by the dog's weight. - **Distribution of Weights**: If the weights of the puppies are relatively close to each other but differ significantly from the dog's weight, the median will provide a better central value that reflects the typical weight of the puppies without being skewed by the dog's weight. - **Interpretation**: If the goal is to understand the typical weight of the puppies, the median would be more representative. If the mean is used, it may suggest a weight that does not accurately reflect the puppies' weights due to the influence of the dog's weight. ### Conclusion: In this scenario, the **median** is likely a better representation of the data set of the weights of a dog and her newborn puppies because it is less affected by the outlier (the dog's weight) and provides a more accurate reflection of the typical weight of the puppies.