Unlike many elections for public office where a person is elected strictly based on the results of a popular vote (i.e., the candidate who earns the most votes in the election wins), in the United States, the election for President of the United States is determined by a process called the Electoral College. According to the National Archives, the process was established in the United States Constitution "as a compromise between election of the President by a vote in Congress and election of the President by a popular vote of qualified citizens." (http://www.archives.gov/federal-register/electoral-college/about.html accessed September 4, 2012).
Each state receives an allocation of electoral votes in the process, and this allocation is determined by the number of members in the state's delegation to the US Congress. This number is the sum of the number of US Senators that represent the state (always 2, per the Constitution) and the number of Representatives that represent the state in the US House of Representatives (a number that is directly related to the state's population of qualified citizens as determined by the US Census). Therefore the larger a state's population of qualified citizens, the more electoral votes it has. Note: the District of Columbia (which is not a state) is granted 3 electoral votes in the process through the 23rd Amendment to the Constitution.
The following table shows the allocation of electoral votes for each state and the District of Columbia for the 2012, 2016, and 2020 presidential elections. (http://www.archives.gov/federal-register/electoral-college/allocation.html accessed September 4, 2012).
Here is a dotplot of the distribution.
What measure of center (mean or median) would you recommend for describing this data set? Why did you choose this measure?
Determine the value of the median for this data set (electoral votes).
Commentary
In addition to providing a task that relates to other disciplines (history, civics, current events, etc.), this task is intended to demonstrate that a graph can summarize a distribution as well as provide useful information about specific observations. With the table provided, the graph and values have context. The purpose of this task is to help students understand that a distribution can be described in terms of shape and center, and also to provide practice in selecting and calculating measures of center.
This task was designed so that it does not require the use of technology. If students have access to technology, you can also consider having students calculate the value of the mean and then comparing the values of the mean and the median for this data set. You could then facilitate a discussion of the effect of outliers on the value of the mean, which would support the choice of the median to describe the center for this data set.