Question

1. how much for that house? the mean and median selling prices of existing single - family homes sold in the united states in may 2014 were $260,700 and $213,600.

a. which of these numbers is the mean and which is the median? explain your reasoning.
b. write a sentence to describe how an unethical politician could use these statistics to argue that may 2014 home prices were too high.

1. baseball salaries, means and medians suppose that a major league baseball teams mean yearly salary for its players is $2.3 million and that the team has 25 players on its active roster. what is the teams total annual payroll? if you knew only the median salary, would you be able to answer this question? why or why not?

Explanation:

Step1: Recall the property of mean and median

The mean is affected by extreme values. In the housing price data, there are likely some very expensive houses (extreme values) that pull the mean up. The median is the middle - value when the data is ordered. So, the higher value ($260700$) is the mean and the lower value ($213600$) is the median.

Step2: Unethical politician's use of statistics

An unethical politician could use the mean ($260700$) to argue that home prices were too high. Since the mean is influenced by high - end expensive homes, it gives a higher - than - typical value.

Step3: Calculate the baseball team's payroll

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Given $\bar{x}=2.3$ (in millions) and $n = 25$. Then $\sum_{i=1}^{n}x_{i}=\bar{x}\times n$. Substitute the values: $\sum_{i = 1}^{25}x_{i}=2.3\times25 = 57.5$ (in millions). If we only know the median, we cannot calculate the total payroll. The median is just the middle - value in an ordered list of salaries. It does not give information about the sum of all salaries (for example, we don't know how much the players above and below the median earn).

Answer:

a. The mean is $\$260700$ and the median is $\$213600$. The mean is affected by extreme (high - priced) homes, pulling it up, while the median is the middle value.
b. An unethical politician could say “The average (mean) home price in May 2014 was $\$260700$, which is too high”.
For the baseball team: The total annual payroll is $\$57.5$ million. If we only know the median salary, we cannot answer the question. The median is the middle value and does not provide information about the sum of all salaries.