Question

Electing the presidentTo become president of the United States, a candidate does not have to receive a majority of the popular vote. The candidate does have to win a majority of the 538 Electoral College votes. Here is a stemplot of the number of electoral votes in 2016 for each of the 50 states and the District of Columbia:

(a) Find the median.

(b) Without doing any calculations, explain how the mean and median compare.

Short answer

Part (a) 8 electoral votes

Part (b) The mean is higher than the median.

Step-by-step solution

Part (a) Step 1. Given information.

The given data is shown below:

Part (a) Step 1. Find the median.

Arrange the given data from smallest to largest:

3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 13, 14, 15, 16, 16, 18, 20, 20, 29, 29, 38, 55

As we know that median is the middle value of a data set. As the given set is odd, the median will be the middle values (26th) of this sorted data:

$M=8$

Therefore, the median is 8 electoral votes.

Part (b) Step 1. Compare the mean and median without doing any calculations.

As we can observe that most of the values are towards the top of the stem plot (corresponding to tiny data values), while a few more uncommon data values are near the bottom of the stemplot (corresponding to bigger data values), the distribution is skewed to the right.

The mean is higher than the median in a right-skewed distribution because the mean is influenced more by the data set's abnormally big data values.