Unfortunately, many learners do not connect the four scales to the correct choice of graph. This problem is especially prevalent for bar graphs and histograms.
Bar graphs should be used for displaying frequencies for nominal data. For review, nominal data is that which can be placed into categories. Gender is an example where the categories are male and female. We could assign numbers such as 0 and 1 for male and female; however those numbers have no quantitative value other than serving as numerical labels.
You can see that the x-axis below uses a nominal variable (gender). The y-axis then is just the mean time studying (fictional data). A key feature of the bar graph is that the bars are not touching each other. This makes it easier to see that that bars are representing separate categories.
Histograms, on the other hand, are for numerical data such as that on the ordinal, interval, and ratio scales. (Actually, one can get away with bar graphs for ordinal data if there are only a few levels such as low, medium, and high. Yes, they are rank-ordered but they can also be viewed as distinct nominal categories.) But what about the previous y-axis variable of study time? In my data, those are numbers ranging from 6 to 23. Those numbers are not nominal categories (unless I go a step further and create categories from the numbers). So, what if I want to get an idea of frequencies for these numbers? I should use a histogram. Usually, the bars will be touching each other. Why is this important? Well, a good reason for histograms is to view the frequencies for numerical data, but an equally important reason is to take a look at the shape of the distribution. If the bars aren't touching, it becomes more difficult to judge the shape.
With this histogram, we can see that this distribution has an odd shape to it. First, we see that one value (23) is not touching the other bars. That's because there are no values between it and the next lowest value. Second, we see that including this 23 (a potential outlier) suggests a distribution that is approaching being normal and bell-shaped while slightly positively skewed.
Note that if we had used a bar graph, we might not even notice this potential outlier of 25. Check this out!
The scaling on the x-axis is misleading. It moves up by twos from 6 to 10, and then the trouble begins. At the end of the x-axis, the value jumps from 15 to 23, but the space between bars is the same as for all others! The bar graph version makes it nearly impossible to determine the shape of the distribution!
*************************
For assistance with statistics,
visit StatRelief
*************************

