Question

a board of governors publishes information on family net worth. in 2010, the mean net worth of families in a particular country was $438.6 thousand and the median net worth was $75.1 thousand. which measure of center do you think is more appropriate? explain your answer. choose the correct answer below.
a. the median because it is not strongly affected by the relatively few families with extremely high net worth.
b. the mean because it takes into account each family’s net worth in the country.
c. the median because it takes into account each family’s net worth in the country.
d. the mean because it is not strongly affected by the relatively few families with extremely low net worth.
e. the mean because it is not strongly affected by the relatively few families with extremely high net worth.
f. the median because it is not strongly affected by the relatively few families with extremely low net worth.

Explanation:

To determine the appropriate measure of center (mean or median) for family net worth, we analyze the properties of mean and median:

• The mean is the average, calculated as the sum of all values divided by the number of values. It is sensitive to extreme values (outliers).
• The median is the middle value when data is ordered. It is resistant to extreme values (outliers).

In the context of family net worth, there are likely a relatively few families with extremely high net worth (e.g., wealthy billionaires or millionaires). These extreme high values would significantly inflate the mean (since the mean is sensitive to outliers), making the mean an inaccurate representation of the "typical" family net worth. The median, however, is not strongly affected by these extreme high values because it only depends on the middle value of the ordered data.

Now let's analyze the options:

• Option A: States the median is appropriate because it is not strongly affected by relatively few families with extremely high net worth. This matches our analysis.
• Option B: Claims the mean is appropriate because it takes into account each family’s net worth. While the mean does use all data, its sensitivity to extreme high values makes it inappropriate here. Eliminate B.
• Option C: Incorrectly says the median takes into account each family’s net worth. The median only depends on the middle value, not all values. Eliminate C.
• Option D: Incorrectly attributes the mean as not being affected by extreme low net worth. The mean is sensitive to extreme values (both high and low), and the problem context is about extreme high net worth, not low. Eliminate D.
• Option E: Incorrectly claims the mean is not strongly affected by extreme high net worth. The mean is sensitive to extreme high values. Eliminate E.
• Option F: Incorrectly attributes the median’s resistance to extreme low net worth. The problem context is about extreme high net worth, not low. Eliminate F.

Answer:

A. The median because it is not strongly affected by the relatively few families with extremely high net worth.