One of the big limitations of two-dimensional graphs is that a single graph ussually can only display two variables. There are times that when it's necessary to display multiple variables. In this video, we discuss a few techniques to do just that. I should emphasize from the off side that, displaying more than two variables on one graph can make understanding and interpreting the graph more challenging. So before deciding on this path, you should determine whether it is indeed necessary. Sometimes, a better approach is to use multiple graphs arranged together to display multiple variables, which are typically called Small Multiples. We will briefly mention them in this video as well. Let me start with a familiar example of scatter plot. As we know, one limitation of a scatter plot is that it only displays the relationship between a pair of variables. However, there are ways to add in more data by creative use of color and bubbles and et cetera. This graph shows a murders per 1,000 population versus burglaries per 1,000 population in the year 2002. And it can be seen that the two are highly correlated. Can we add a third-dimension to the graph? The answer is yes, there are several different ways, for example, you can choose to color code the points in the scatter plot based on some criteria. Sometimes color intensity is used to encode data. For example, we can choose to use a default color for data points that are from a state with larger population. Another way is to resize the data point based on other data column which is what we did here. Here the size of the circle is used to encode the population size. This plot is referred to as bubble plot in Excel. But add in a certain variable population to this graph, we see that the states with larger population also tend to have higher murder rate and burglary rate. This insight cannot be easily shown if we did not have the third dimension in the data. It should be mentioned that the graph with a third dimension is harder to understand. So even though you can add a third dimension, you should only do it when it absolutely necessary. Another use for technique when displaying multiple variables is to use a secondary vertical axis. This can be useful, for example, when the scale of the variables are different or the measurement unit is different. This graph shows a murder rate and burglary rate data in Excel. When we use a bar graph to display the data, the murder rate data can be hardly read as the burglary rate data is much larger in scale. This issue can be solved by adding a secondary vertical access and changing the chart type of burglary rate from bars to a line. Sometimes using multiple side by side plots is preferred to showing all data in the same graph, we call such a design a small multiples. Perhaps the most well-known small multiples design is a side by side boxplot which are commonly used to compare distributions for related data. We can also have side by side histograms, bar charts or scatter plots as well. They are usually quite effective for comparison. With that aspect of small multiple design, we need to ensure that the graphs are consistent, arranged in a right way for easy comparison, I mean the right sequence. By consistency, we mean that the graphs should have the same chart type, axis scale, color scheme, et cetera. In consistence graph in a small multiple can be confusing and difficult to understand. One common issue is that, by default, Excel does not use the same axis ranges when we create multiple graphs. We therefore need to manually change the axis ranges to match. Otherwise, our side by side graph might leave a wrong weird impression. The graphs should also be arranged in a way so that the intended comparison can be easily done. One of the primary decision is whether to arrange the graphs horizontally or vertically. You might have to try several different layouts. Finally, the graphs should be sequenced properly. Typically, the graphs are linked by an index variable, for example, age group, gender, et cetera. Sometimes, there is a natural order to follow. In the case of age groups, it is common to order from the youngest to the oldest. Not following this order can cause confusion.