Final answer:
The appropriate measures of center and variability for the number of hits by players in each of the two leagues depend on the shape of the distributions. For symmetrical and bell-shaped distributions, the mean and standard deviation are often suitable measures. For skewed or outlier-dominated distributions, the median and interquartile range may be better measures to summarize the data.
Step-by-step explanation:
When analyzing the shape of distributions, we can select the appropriate measures of center and variability based on the characteristics of the distribution. For distributions that are approximately symmetrical and bell-shaped, such as the normal distribution, the mean and standard deviation are often suitable measures of center and variability respectively. On the other hand, for distributions that are skewed or have outliers, the median and interquartile range (IQR) may be better measures to summarize the data.
In the case of the number of hits by players in each of the two leagues, we would need to examine the shape of the distributions to determine which measures are appropriate. If the distributions have a symmetrical and bell-shaped shape, we can use the mean and standard deviation. However, if the distributions are skewed or have outliers, we should use the median and IQR.
It is important to note that the selection of measures of center and variability depends on the specific characteristics of the distributions and the context of the data.