Question

As part of its 20th anniversary, a company held a party to celebrate. In an informal survey, a local newspaper reporter asked 100 of the attendees about their income. The reporter

computed the mean income of the 100 attendees to be $205,652. In the article published by the local newspaper, the reporter was quoted as stating. ""The members of the company are
paid quite well. Last year, they had a mean income of $205,652

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: The reporter's manager felt the individuals who attended the party may be different from the company as a whole. A more detailed survey of the company was planned to determine a better estimate of income. The staff developed two methods based on the available funds to carry out the survey

Method 1. Send out an e-mail to all 5,365 members of the company and ask them to complete an online form. The staff estimates that at least 750 members will respond.
Method 2. Select a simple random sample of the employees and directly contact the selected individuals by phone. Follow up to ensure all responses are obtained. Because method 2
requires more time than method 1, the staff estimates only 400 employees can be contacted using method 2.
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

Answer 1

The median is a better measure than the mean of income in the presence of outliers, providing a more accurate reflection of the typical income. For a more detailed survey, Method 2 is advantageous due to its unbiased simple random sampling, even with a smaller sample size compared to the potentially biased self-selected responses of Method 1.

Step-by-step explanation:

Understanding Measures of Central Tendency and Sampling Methods

When considering the mean income of the company's members, using the median as the measure of central tendency provides an advantage in situations where the dataset includes outliers. For example, if there is a significant disparity in incomes such that there are many typical incomes at $30,000 and an outlier at $5,000,000, the mean would be skewed by the high outlier value. Meanwhile, the median, which is the middle value when all incomes are ranked from lowest to highest, would not be affected by this extreme value and would give a better representation of the typical income.

In the scenario where a more accurate estimate of the income is sought through surveys, comparing Method 1 and Method 2 indicates that Method 2 might yield more reliable results despite the smaller sample size. This is because a simple random sample (Method 2) ensures that every member has an equal chance of being selected, leading to a more representative sample of the company's population. In contrast, using an online form (Method 1) may result in non-response bias if certain segments of the population are less likely to participate, skewing the results based on who chooses to respond.