In this video we're gonna go over how to construct a frequency polygon. A frequency polygon is a graph
that provides a visual representation of a data frequency distribution. It uses a line
that connects the frequencies of the classes at the midpoints of the classes. In a past video we
discussed what a frequency distribution is, real quick, you have a dataset, you break the data down
into classes or intervals, you tally up how many data points are in each class, and you write that
number down, which is the frequency. Now we want to take the data that we organized and summarized in
the frequency distribution table, and show or display it in a graph form. So the first thing
we're going to do is draw an x and y axis. For the x axis I'm gonna put this little squiggle in
near the beginning of the line and I'll explain this later in the video. Next we need to label
the zeros, which is going to be where the x and y axes meet. Now we need to label both of these
axes. The y axis is easy, that's going to be the frequency or the amount of data points in each
class. If you look at the table, the largest number in the frequency column is 25 for the fourth class.
So knowing this, we can draw this line, and mark it as 25, somewhere near the top of where our y axis
ends. Then we're gonna mark 20, 15, 10, and 5, on the y axis. Make these so that they are the same distance
from one another or at least within reason if you're drawing this by hand. The x axis is gonna
represent whatever the data is, so let's say this data represents sales. But before we label the x
axis we need to calculate the class midpoints for each of the classes. The formula for finding
a midpoint of a class is the lower class limit plus the upper class limit and take that result
and divide by 2. So, for class 1, the lower limit is 126, add that to the upper limit of 174, and we get
300. Take that and divide by 2, and we get 150 as the midpoint for class 1. Continuing this process
for the remaining six classes, we get 199, 248, 297, 346, 395, and 444. And you can see the results in
this table. Now that we have the class midpoints we can label the x-axis. This little squiggle here
basically means a broken axis, or it lets the viewer know that there are some values kind of
scrunched up here. We can start by marking the value of the midpoint of class 1 somewhere to the
right of our squiggly line. So, 150 right here. Next we'll mark the midpoint of class 2 to the right of
the mark for the midpoint of class 1, let's say right here, and now the midpoint of the third class.
When we mark this we want to mark it so it has the same distance or width, within reason, as the width
between the midpoint markings for class 1 and class 2, so right about here. And when we continue this
process so all of the midpoints of all the classes have been marked with the same widths between them.
Next we need to plot the points for each of the classes. We're gonna use the midpoints as the
x-axis or horizontal values, and the frequencies for the y axis or vertical values. So for class 1
we have a frequency of 5 and a class midpoint of 150. We find this value on the graph, where these
two values intersect and plot a point there. For class 2 we have a frequency of 5 and a midpoint of
199, again, mark the point of intersection with a dot. And you would continue this process for the
remaining 5 classes. Now that we have all of our points plotted, we'll connect the dots from class 1
to class 2, to class 3, and so on, until we have all the points connected. One last thing that we need
to do is draw a line back to the x-axis at the beginning and end of the graph. At the beginning of
the graph we're gonna pick a point on the x-axis that has the same width as the width between the
other markings on the graph, so, right about here. And we'll plot a point and connect the line from
this point to the first point. At the end of the graph we'll use the same process, plot a point on
the x-axis that has the same width or distance as between the other markings and then connect this
point to the previous point. And va-la, our graph is complete. All right my friends, hopefully you got
something out of this video, I do have more videos right there for you, till next time, I am outta here.