Question

A family is looking for a new home. The family is comparing homes in two towns. The median home price of Town 1 is ​$300 comma 000. In Town 2 the median home price is ​$245 comma 304. Based on the median home prices of each​ town, what inference can be​ made? What else might a person conclude from the median​ values?
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Part 1
Which of the following is a correct inference based on the median​ values?
A.The homes in Town 1 and Town 2 are similarly priced.
The homes in Town 1 and Town 2 are similarly priced.
B.The homes in Town 1 are more expensive.
The homes in Town 1 are more expensive.
C.The homes in Town 2 are more expensive.
The homes in Town 2 are more expensive.

Answer 1

Correct choice: B. The homes in Town 1 are more expensive.

Explanation and caveats:
- The median home price in Town 1 ($300,000) is $54,696 higher than in Town 2 ($245,304), so the typical (middle) home in Town 1 costs more.
- What you cannot conclude from the medians alone:
- You cannot say every home in Town 1 is more expensive than every home in Town 2.
- You don’t know anything about price spread, variability, or outliers (ranges, quartiles, standard deviation).
- You don’t know sample sizes or whether the medians come from comparable data sets (same time period, types of homes).
- You don’t know differences in home size, age, condition, neighborhood, taxes, or other factors that affect price.

What else to check:
- Look at mean price, quartiles or a boxplot, range, number of sales, and distribution shape to get a fuller picture.
- Compare home characteristics (square footage, bedrooms, lot size) and local costs (taxes, insurance, utilities) before deciding which town is more affordable or a better fit.