Question

1.A- The government of River City, population 750,000, wants to know how best to allocate funds to serve its residents. Right now it is trying to determine whether to continue funding the "Concerts in the Park" summer music series. To gather data, it hires a firm that specializes in marketing research via telephone. The firm makes 200 calls asking respondents how often they attend the shows.

The size of the sample in question here is relatively (large/small) and the data (are/are not) likely to have significant outliers or large gaps in the values.

What is the best measure of centrality to use in this case? A-Mean ; B-median; C-Weighted mean ;D-Mode

1.B-Otis needs to know how many people his elevators can carry safely. He already knows how much weight they can bear before malfunctioning, so he needs to divide that by the average weight of a person. He uses a large pool of data from the federal government to calculate that average, which he then uses to estimate the largest group of people his elevators will safely accommodate.

The size of the sample in question here is relatively (large/small), and the data(are/are not) likely to have significant outliers or large gaps in the values.

What is the best measure of centrality to use in this case? A-Mean ; B-median; C-Weighted mean ;D-Mode

1.C-The Bakunin Banking Corp. employs 32 people. Upper management includes the CEO, who makes about $1.2 million per year with bonuses; the CFO, who earns $850,000; and three department heads, who each make between $700,000 and $750,000. The company also has two IT staff members, who each make $80,000. The rest of the employees work as clerks and earn between $20,000 and $27,000 dollars. The clerks are thinking about unionizing, and in making their case, they want to emphasize the disparate incomes at the firm.

The size of the sample in question here is relatively (large/small), and the data(are/are not) likely to have significant outliers or large gaps in the values.

What is the best measure of centrality to use in this case? A-Mean ; B-median; C-Weighted mean ;D-Mode

Answer 1

1.A) The best measure of centrality to use in this case is: D- MODE

The government should allocate funds to "Concerts in the park" based on how often the maximum population (highest frequency) attend those shows. This can be identified using "mode".

1.B) The best measure of centrality to use in this case is: A- MEAN

Since, Otis knows how much total weight his lift can bear before malfunctioning, we just need simple average to estimate the group of people his elevator will safely accommodate. And because he has access to data from federal govt., which is true representation of population, simple average is the best measure.

1.C) The best measure of centrality to use in this case is: B- MEDIAN

Since there are few extreme values (salary of CEO and CFO) in the data, median is unaffected by such outliers. Median is also preferred where there are some missing or undetermined values in the data (no. of clerks). Overall it would tell us how many employees earn more and less than the median/ middle value of salaries which is a good indicator of income disparity at the firm. If more people earn a salary less than the median income, there is large income disparity in the firm and clerks' claim would be valid.