So far, when we wanted to display the data in a frequency distribution, we've used a histogram, which is definitely our most common option, but not actually our only choice when we wanna display that type of data. In fact, sometimes you might be asked to create a frequency polygon instead. Now I know the name frequency polygon sounds a little scary, but in this video, we're gonna be creating our own frequency polygon, and I think you'll see that they're pretty straightforward. In fact, they're very similar to histograms. They show the exact same data, which means they allow us to see the frequencies across classes.
The difference is that they use points connected by segments as opposed to bars to show the frequency, but, honestly, that's it. Let's take a peek at our example to see how this works. As you'll see on the table, we've been given data on the age distribution of riders on a public bus, which we've started to use to create a histogram over here. Remember that the frequencies of the classes can be seen in the heights of the bars. For example, the frequency of our first class is 6, so the height of our first bar is also 6.
The frequency of the second class is 8, so the height of the second bar is also 8. We're gonna do the same thing for our frequency polygon plotting points instead of making bars. The frequency of the first class is 6, so I'm gonna come over here to that first tick mark and plot a point with a y-coordinate of 6. And I'm gonna do the same thing for my next class. My next frequency is 8, so I'm gonna come over here and plot a point with a y-coordinate of 8.
My next class has a frequency of 7, so I can come over here and plot a point with a y-coordinate of 7. And finally, my last frequency is 5, so I'm gonna come over here and plot a point with a y-coordinate of 5. Now that I have all my points plotted, I'm just gonna connect them with segments. I'm gonna connect my first point to the x-axis on the left, then I'm gonna connect each of my points over here with segments, and finally connect my last point to the x-axis on the right. And that gives me the shape of my frequency polygon.
At this point, let's talk axes. So my y-axis for the frequency polygon is exactly the same as my y-axis for the histogram, and this will be true all the time. They both wanna display frequencies, and, also, the same scale is gonna work for the exact same data. For the x-axis, we also want those to be the same. Remember that for histograms, we label the x-axis with our class midpoints, and we can find those class midpoints by adding the lower and upper limit of a class and dividing by 2.
For example, in our first class, we have a lower limit of 0 plus an upper limit of 24 divided by 2 gets us 12. So our first class midpoint is 12. Now our other class midpoints have already been computed for us, but feel free to pause the video and do them on your own using the formula. Once you're satisfied, why don't you come over and label the x-axis 12, 37, 62, and 87 with those class midpoints. Now my histogram is ready to be interpreted.
I can see that my first bar is labeled with 12 on the x-axis and has a height of 6. That means that the first class with midpoint 12 has a frequency of 6. I'm gonna label the x-axis of my frequency polygon the same way and also interpret it the same way. So I'm gonna label with my class midpoints 12, 37, 62, and 87, and I'm gonna interpret my points in the same way. I noticed this first point has x-coordinate 12 and y-coordinate 6.
That means that the class with midpoint 12 has a frequency of 6. Now frequency polygons can get confused with line graphs, but they are not the same thing. We are not saying that there are exactly 6 people of exactly age 12, but that there are 6 people who are between the ages of 0 and 24, that class that has midpoint 12. Awesome. The last thing we wanna talk about here is skew.
When it comes to finding skew in a histogram, we always look for the peak of the histogram. Then we check for tails. If it has a left tail, it has left skew, a right tail, and it has right skew. And if it has no tail, then it has no skew. For frequency polygons, we're gonna approach it the same way.
So I'm gonna start at the peak of my frequency polygon, which happens at class with midpoint 37 and frequency 8. It's just that highest point. Then I'm gonna check on either side of that peak to see if it extends a lot further to the left for left skew, a lot further to the right for right skew, or about the same in both directions. I notice here that it doesn't really extend much further to the left or to the right, so I can confidently say that this data is not skewed. Awesome job.
If you're feeling ready, why don't you head on over to the practice?
