The graphical display with the relative frequencies along the vertical axis that may be constructed for quantitative data is

The graphical display with the relative frequencies along the vertical axis that may be constructed for quantitative data is known as a Histogram.

Here are the steps to construct a histogram:

1. Identify the range of the data: The range is the difference between the highest and lowest values in your data set.

2. Divide the range into classes (also known as bins or intervals): The number of classes might depend on the nature of your data, but a common rule of thumb is to take the square root of the number of data points.

3. Count how many data points fall into each class: This is the frequency of each class.

4. Draw the bars: On a graph, draw a bar for each class. The height of the bar corresponds to the frequency of the class. The width of the bar corresponds to the class interval.

5. Label the axes: The horizontal axis represents the classes and the vertical axis represents frequencies.

Remember, the key characteristic of a histogram is that it uses area to represent frequency and it deals with quantitative data.