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Identifying Measures of Center on a Graph

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Source: All images created by Dan Laub

[MUSIC PLAYING] Hi, Dan Laub here. And in this lesson, we're going to discuss identifying measures of center on a graph. But before we do so, let's discuss the key objective for this lesson. By the end of this lesson, we should be able to identify the mode on a graph. So let's get started.

Remember that there are three measures of center-- mean, median, and mode. Representing these measures of center on a graph can help communicate information visually by summarizing and organizing the data set so that one can communicate something meaningful with the data. Now, let's take a look at a quick bar graph here just to kind of refresh your memory a little bit.

So remember with a bar graph is we have a horizontal axis. And it gives us what our variable is. We have a vertical axis which largely tells us how many of a particular observation there are. The individual bars are of a certain height based upon how many observations of a specific value of the variable exist.

Now we will discuss identifying mode on a bar graph and a histogram. Of the three measures of center, mean, median, and mode, the mode is simply the value that occurs the most often. The median is the middle value, where half of the other values are larger than the median, and half are smaller. And the mean is the average of a set of data.

Two graphs that are often used in statistics are bar graphs and histograms. In a bar graph, the mode is the value on the horizontal axis with the highest bar, such as this. Histograms, on the other hand, show data grouped together in intervals. This being the case, we cannot state precisely where the mode is. In the event that one has continuous data, it is possible that all of the data are unique, and there is no true mode.

The mode is approximated by saying that is in the center of the tallest bar. So let's look at a couple different examples here. As you can see in this example, we have a bar graph that illustrates the grade distribution for a particular exam. And so you can clearly see the tallest bar in this particular graph happens to represent the grade of a C, in which there are 11 C's out of the entire class. This value would be considered the mode because it does occur the most often in this data set.

The next example I want to show you has to do with the thermostat setting that would existence in, say for instance, a group of homes. In this particular instance, we see a histogram that represents the different ranges. And so the ranges go from anywhere at the low end of 60 degrees Fahrenheit all way up to greater than 75 degrees Fahrenheit. One significant aspect of a histogram are the endpoints of the ranges that we see illustrated on the horizontal axis.

So let's look at the range between 63 and 66 degrees Fahrenheit. It's represented by the orange bar that you see there that has 16 different observations. And what this is telling us is that if the temperature is above 63 degrees Fahrenheit, up to 66 degrees Fahrenheit, it's going to fall within this range. So 63.1 degrees would fall within this range, as would 64 degrees, or 65.8 degrees. It's going to be up to that particular point in which is going to fall in that particular range.

The first range we see here is between 60 and 63 degrees Fahrenheit. The next range, 63 to 66 degrees, 66 to 69, 69 to 72, 72 to 75, and then anything over 75, of which there are 17 homes that have their thermostats set above 75 degrees Fahrenheit. And in this case, we clearly see that the highest value, the highest bar here, is 24. And that falls between the range of 69 and 72.

And so in a case like this with a histogram, we would say that the mode is going to be the halfway point between 69 and 72 degrees Fahrenheit. Or in this case, 70 and 1/2 degrees Fahrenheit. So let's just take a quick look at the objective of this lesson to make sure that we did what we said we were going to do. We wanted to be able to identify the mode on a graph, which we did. We looked at a bar graph. We looked at a histogram. And we identified the mode on both of those. So again, my name is Dan Laub. And hopefully, you got some value from this lesson.