Final answer:
The mean is particularly sensitive to extreme observations (option a), which can significantly affect its value. The median is less affected by outliers and is often a better measure for skewed distributions. The Law of Large Numbers suggests that larger sample sizes will result in a mean closer to the population mean, despite the presence of outliers.
Step-by-step explanation:
The mean is particularly sensitive to extreme observations in a distribution, making option (a) the correct answer to the question. Extreme values, also known as outliers, can significantly distort the mean because it includes all values in its calculation. This characteristic of the mean is in contrast to the median, which is less affected by outliers since it is the middle value when all observations are ordered from least to greatest.
The median, therefore, is a better measure of central tendency for skewed distributions or when outliers are present. Influential points, which are extreme values in the horizontal direction, can also impact the slope of a regression line and should be carefully assessed for their effect on the dataset.
The Law of Large Numbers explains that as sample sizes increase, the sample mean tends to get closer to the population mean. However, even in large samples, if extreme observations are present, they can still affect the mean. Sampling variability and variability induced by outliers are important concepts to consider when analyzing data.