In this video we're gonna go over how to construct an ogive graph. An ogive is a graph that provides
a visual representation and uses a line that connects the cumulative frequencies, at the upper
class boundaries, for the classes in a frequency distribution. In a past video we discussed what
a frequency distribution is, real quick, you have a data set, you break the data down into classes or
intervals, you tally you up how many data points are in each class, and you write that number down, which
is the frequency. So the first thing we're gonna 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 that later in the video.
Next we need to label the zeros, which is going to be where the x and y axes meet. Next we need to
label both of these axes. The y axis is going to be the cumulative frequency, and cumulative basically
means the total amount of something, in this case the total amount of data points in the data set,
which is 75. So high up on the y or vertical axis we're gonna mark 75, now we're gonna make 7
more marks going down 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. And we're gonna label them going down by
10, so 65 is the first mark below the 75, then 55 and on down to 5 for the last mark. The x or
horizontal axis is going to represent whatever the data is. So let's say this data represents
sales. For the x axis we're gonna use upper class boundaries to mark it, so we need to calculate
them. Since our data is all whole numbers we can simply add 0.5 to the upper limits of each class.
So for class 1, we get 174 plus 0.5 which equals 174.5, for class 2 we get to 223 plus
0.5, which equals to 223.5, and we continue the rest for the remaining classes as you
see in this table here. One other thing that we're gonna do is calculate the lower class boundary
for class 1. For this we're going to subtract 0.5 from the lower class limit of class 1, 126,
to get 125.5. Now that we have the upper class boundaries and the lower class boundary
for the first class, 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. Somewhere to the
right and near the squiggle, we can mark the lower class boundary for class 1, 125.5.
Next we'll mark the upper class boundary for class 1, 174.5, here. Then
223.5, the upper class boundary for class 2 here, and continue on marking all the
upper class boundaries for the rest of the classes on the x-axis, as you see here. Again make these so
that they are the same distance from one another or at least within reason if you're drawing this
by hand. Next we need to calculate the cumulative frequencies for each of the classes. So for the
first class we need to find the total amount of data points in the data set that are less
than the upper class boundary of class 1, which is 174.5. We can see in the
frequency distribution table that there are 5 values that satisfy this. For the second class we
have an upper class boundary of 223.5, and we can see from the table that
there are a total of 10 values in the data set that are less than this. 5 in class 1, and 5
in class 2. For the third class there are 30 values less than 272.5, and
we continue this process for the remaining classes. For the seventh and final class we should have 75,
because that is a total number of data points in the data set. Now we're ready to plot the points on
our graph starting with the lower class boundary for class 1, 125.5, which
has a cumulative frequency or y-value of 0. Next is the upper class boundary of class 1, 174.5
here on the x-axis, where we have a cumulative frequency of 5, so we find our point
of intersection, x equals 174.5, and y equals 5, and plot the next point.
Next would be the upper class boundary of class 2, 223.5, and our cumulative
total, or y value equals 10 here. Again, find our point of intersection and plot the next point. And
we continue this process for the remaining classes. Now that we have all of our points plotted, we will
connect the dots from our zero value to class 1, to class 2, to class 3, and so on until we have
all the points connected. 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.