Question

Part A: What is a statistical advantage of using the median of the reported incomes, rather than the mean, as the estimate of the typical income?

Part B: Which of the two methods would you select for estimating the average yearly income of all 5,365 employees of the company? Explain your reasoning by comparing the two methods and by describing the effect of each method on the estimate.
a) Method 1 should be selected as it provides a larger sample size.
b) Method 2 should be selected as it provides a more representative sample.
c) Both methods are equally valid for estimating the average yearly income.
d) More information is needed to make a selection between the two methods.

Answer 1

Part A: The statistical advantage of using the median over the mean is that the median is less sensitive to extreme values or outliers in the data.

Part B: I would select Method 2, as it provides a more representative estimate of the average yearly income by mitigating the impact of outliers.

Step-by-step explanation:

Part A: The median is a measure of central tendency that is not influenced by extreme values, making it a robust statistic. In cases where the distribution of incomes is skewed or contains outliers, the median provides a more accurate representation of the typical income. Unlike the mean, which can be heavily influenced by extremely high or low values, the median is determined by the middle value in a sorted dataset. This makes it a better choice when dealing with income data that may have significant variations.

Part B: Method 2 should be selected for estimating the average yearly income of all 5,365 employees. The median is a more suitable measure in situations where the dataset may have extreme values, such as a few employees with exceptionally high or low incomes. Using the mean (Method 1) in such cases could lead to a skewed estimate, as it is sensitive to outliers. The median, on the other hand, is resistant to the influence of outliers, providing a more reliable measure of the central tendency in the presence of extreme values.

In conclusion, both parts A and B emphasize the importance of the median in scenarios with potentially skewed income distributions. The robust nature of the median makes it a preferred choice for estimating the typical income, especially when dealing with datasets that may contain outliers.