Source: All graphs created by Dan Laub
Hi. This is Dan Laub, and in this lesson we're going to discuss matching the type of data with the correct graph. And before we get started, let's go over the objective for this lesson. The objective here is to be able to identify the correct type of graph to use with specific categories of data. So let's get started. Two commonly used graphs in statistics are bar graphs and histograms.
Bar graphs show the data for nominal or ordinal variables, while histograms show the data for interval or ratio variables. Remember that nominal variables indicate categories, such as gender. Ordinal variables indicate order, as in first, second, third, and so forth. Interval variables provide numbers so that the difference between the two values can be measured, and ratio variables are interval variables, where the only difference is that a value of 0 does mean that something does not exist.
So for example, look at the graph you see in front of you. This is a bar graph, and this bar graph represents test scores in a particular class. And so we have the common values, A, B, C, D, and F. And you'll notice how they go from left to right. They started at F, D, C in the middle, then B, and then A on the far right side. And each bar indicates how many of this particular grade there were in this particular class for this exam.
And so if we were to use a histogram to demonstrate this particular data set, we would not necessarily be accurately representing what we were trying to illustrate with the bar graph, and the reason is because a histogram is better used for ranges of data, where there's actually something where there's an interval, as opposed to just an actual nominal variable, which in this case would be the letter grade.
And so a histogram would not be the correct manner to go about illustrating this particular type of data. Recall that in step eight of the experimental method, process data must be represented so that it can be shared with others. There are many different ways to represent data, and one of which is to use a bar graph. Bar graphs are used from nominal and ordinal variables.
With nominal variables, the categories are listed on the horizontal axis in any order. For ordinal variables, the categories are listed on the horizontal axis in order from smallest to largest. As you see on the graph in front of you, we have a bar graph that represents the handedness of college students. So in a hypothetical survey of 1,200 college students, it turns out that 243 are left handed, 774 are right handed, and the other remaining 98 are ambidextrous, or they could use either one.
And what we're seeing here is individual bars that represent the height of those particular values. So in other words, depending on how many observations there are of each particular one of these nominal variables, such as left handed, right handed, or ambidextrous, it's going to represent how high the bar actually is. And on the horizontal access, you'll note that we have the three options-- left handed, right handed, and ambidextrous. And those are the three choices.
One thing to note here is that the bars do not touch one another, and the reason they don't do that is because they have unique categories. Since there are different ways represent data, another method we can use is a histogram. And you'll notice the histogram we see here represents the high temperature in Orlando, Florida for the month of November 2015.
And what we have done here is broken it down into specific ranges. And so on the far left you'll notice that the legend at the bottom of the graph says this would be for the high temperature being below 70 degrees Fahrenheit. The next category is anywhere between 70 and 75 degrees Fahrenheit. The third category between 75 and 80 degrees Fahrenheit, the fourth one between 80 and 85 degrees Fahrenheit.
The fifth one between 85 degrees and 90 degrees Fahrenheit, and the last category would be anything greater than 90 degrees Fahrenheit. And you'll notice of the 30 days in November, as we measure here on the vertical axis the number of days, the majority of the observations fell within the range between 80 and 90 degrees Fahrenheit.
There were a few days when it was relatively cool. There was one day which was above 90 degrees, but for the most part you see how, with 11 days each on the ranges of 80 to 85 and 85 to 90, that the majority of observations fell within that specific range. Histograms are used for interval and ratio variables, and while they also have bars, the bars actually touch in this case, since the horizontal axis shows values that can be subtracted to find the difference between two sets of variables or intervals.
So in this case we can clearly see the difference between 87 degrees and 82 degrees Fahrenheit, just as much as we could between 78 degrees and 73 degrees Fahrenheit. Typically with a histogram, the endpoints would be defined as the boundaries between the two ranges, and so with a hypothetical range of 80 to 85, as you see here highlighted in yellow, that would include the 80 degree mark, and include everything up to the point just short of 85.
Once you reach 85, it would be in the next range, and that would continue up to just short of 90. And anything above that would include 90 and above. And so the endpoints, we typically look at the bottom value as being included in the range, whereas the top value would not. We will cover a lot more information about histograms in a future tutorial. So notice how the bar graphs in the histograms are different from one another.
With the bar graphs we see individual categories for nominal or ordinal variables. And with a histogram, we see categories that represent interval or ratio variables. And in this case the bars actually touch each other, because they represent a range, and not individual categories. And so let's do a quick review, just to make sure we covered the objective for this particular lesson.
We wanted to be able to identify the correct type of graph to use with a specific category of data, which we did. We went over the fact that nominal and ordinal variables are represented using a bar graph, while ratio and interval variables are represented using a histogram. So again, my name is Dan Laub, and hopefully you got some value from this lesson.