Exercise 19 Page 723

We are told that two lanes of opposing traffic can be divided by a strip of land called a median.

Note that a median is in the middle of a road and between lanes of traffic. On the other hand, we can also talk about the median in terms of data sets. We are already given that the median divides a data set in some way.

Since the median is in the middle part of the road, let's consider dividing our data set in the middle as well. To do so, let's write the data values in increasing order. Then we will choose the value in the middle.

In this example, choosing the middle value is straightforward because we have exactly 4 items on the left and 4 items on the right of the median. A small issue occurs when we have an even number of elements in the data set.

In this situation, we have two candidates for the middle value. Therefore, to obtain the median, we calculate the average of the two middle values. Recall that the average of two numbers is the sum of these numbers divided by 2.

Once again, the median divided the data set into two parts, both of which consisted of 4 data values. Finally, we can conclude how the median divides a data set.

Extra

Different Meanings of Median

We have already found that the median has at least two different meanings.

1. The strip of land that divides the two sides of opposing traffic.
2. The middle value in a data set with values in an increasing order.

However, the median can also describe a triangle.

A median in a triangle is a line segment between the midpoint of one side and the opposite vertex.