• When launching the lesson, it can be tempting to go down the rabbit hole of explaining the features of mortgages and interest rates. Instead, we recommend simply explaining that when you pay a mortgage, you own the home, and home values tend to go up over time. This is how many middle class families have built wealth over time and achieved the American Dream. Therefore, it’s concerning that fewer young adults are buying homes. Why is that? And how does this trend affect their prospects at the American Dream?
• You can share with students that, for data sets with an odd number of values, a specific data value will be the median. However, for data sets with an even number of values, the median will fall between two data values. So, the median will be the average or midpoint of the two most central data values.
• Students can use the formula n+1 2 as a shortcut for finding the middle position (the median’s position) of a data set. For example, for a data set with n = 5 values, the middle position is at 5+1 2 = 3 → the 3rd value in the data set. For a data set with n = 6 values, the middle position is at 6+1 2 = 3.5 → between the 3rd and 4th values in the data set.
• One nice connection to make for students is the relationship between percentiles and quartiles, where Q1 approximately corresponds to the 25th percentile and Q3 approximately corresponds to the 75th percentile.

First, download this lesson's Handout Key and read through its Discussion Question section. Then, check out our model discussion norms and the additional background notes below.

• When motivating the Discussion Question, rather than providing a technical explanation of supply and demand, using a simple example may be helpful: “Imagine five people (buyers) are moving to a small town, where there’s only one home for sale (seller). The buyers will try to outbid one another for the home, moving the price up. However, if there are 10 homes for sale, the sellers may lower their prices to outcompete one another and attract a buyer. So, having more homes on the market helps drive prices down.”
• Depending on the context in which you teach, you may find that your student population has a lopsided opinion on this Discussion Question. As a facilitator, it’s valuable to encourage students to voice the “other side,” so that students have a robust discussion that mirrors the broader civic discussion on this topic.

• The small sample of home prices from 1970 was taken to match population mean ($26,300) and median ($22,300) home price sales from 1970 in the United States, according to estimates from the Federal Reserve.
• According to the Bureau of Labor Statistics’ inflation calculator, $1 in 1970 had the same buying power as about $8 in 2024. This means that the growth in U.S. median income over those years ($9,853 in 1970 to $90,100 in 2024) has only slightly outpaced inflation. Meanwhile, the growth in median home price ($22,300 in 1970 to $423,000 in 2024) has far outpaced inflation. Source for home price data: Federal Reserve. Source for income data: US Census Bureau (1970 Table 17 and 2024 Table A-1).
• Data sets of home values and incomes tend to have a right skew. Hence, the median is often a more useful measure of center for these variables than the mean. This may be a helpful point to reference during the next lesson in the course sequence, which specifically explores the median’s resistance to outliers and skew.

• For small data sets like the one discussed in this lesson, calculating measures of center and spread is often unnecessary. Instead, creating a dotplot of the data set and describing it could be considered a more useful analysis. However, when first learning about summary statistics, finding each measure of center and spread on a small data set is conceptually helpful. That’s why this lesson utilizes a small data set.
• We provide an optional video that shows how the standard deviation of a small data set is calculated manually. The video helps motivate the formula for the sample standard deviation. However, students sometimes have two questions about the standard deviation formula. Note that the following questions and responses are outside the scope of the AP Exam.
• Why do we square the differences to get rid of negatives? Why not just get the absolute value? There are two central reasons for this: i) Squaring emphasizes larger differences, which can be helpful for surfacing outliers. ii) Squares have nicer mathematical properties than absolute values. In particular, models that try to minimize the standard deviation often take the derivative of the standard deviation function. It’s much easier to find the derivative of a square than an absolute value. Check out a more thorough discussion of this topic here.
• Why do we divide by n - 1, instead of simply dividing by n? The reason is based on the concept of degrees of freedom. When calculating the sample standard deviation, we use the sample mean and every data value. However, with the sample mean in hand, we don’t actually need to be given every data to recreate the full sample. The final data value can be inferred from the sample mean and the remaining n - 1 data values. Hence, there are only n - 1 varying pieces of information in the standard deviation formula, or n - 1 degrees of freedom. This is why we divide by n - 1. A fuller discussion can be found here. We’ll explore the concept of degrees of freedom later in the course.