Transcription
In this lesson, we're going to discuss how graphs can be a bad representation of our data. Some graphs are bad in the sense that they contain errors. Some are bad because they are typically correct but misleading. And it's important to develop the ability to recognize bad graphs and identify exactly how they are misleading.
Let's take for example a graph that has a non-zero axis. So, if we don't start at zero on either or both of the axes, it could be misleading or make a difference that looks exaggerated. So, if we look here at this graph, we see that if we start our y-axis at 53 instead of zero, it really makes Democrats look to be having a very large difference compared to the Republicans and Independents. But if you change that to a zero axis, then the difference doesn't look quite as large. So, the first graph was very misleading as far as the gain the Democrats have on the Republicans to the Independents.
Pictographs can also have drawings that create false impressions and distort differences. For example, if you triple each side of a square, the area increases by a factor of nine. See here, if you triple each side of a cube, the volume increases by a factor of 27. So, therefore, pictographs using areas and volumes can be very misleading.
Take for example this daily oil consumption picture between the US and Japan. The graph uses cylinders to represent barrels of oil consumed by the United States and Japan. Does the graph depict data fairly? Why or why not? Well, 20.0 versus 5.4. This is just over 1/4 of 20. So, technically, four of these little cylinders, just about four of those cylinders, should fit into the US. But when you copy and paste the cylinder and paste it into the 20, you can see that it definitely is not to scale. If I put four of these little barrels into it, the US is over exaggerated compared to the 5.0, 5.4. I can fit probably six or seven of these Japans into the US. So, it is over exaggerated and not a good representation of the data.
This sideways bar graph for the annual income for groups with different educational levels has the same width bars. So, that part is correct. But the graph is too busy. It's too difficult to understand. This graph is misleading because it depicts one-dimensional data with three-dimensional boxes. Again, we'd run into that problem. If I was to duplicate this and put it into this box, the non-high school diploma to the advanced degree, the percentages, the ratios of the amount of income does not relate to the size of these boxes.
This is a better way to represent the data of the annual income for groups with different educational levels. It's not crowded by pictures. It's, uh, and it's a paragraph. You have your annual income on the side and your educational level underneath.
Here's some key points to keep in mind when you're analyzing a graph. Examine the graph to determine whether it is misleading because an axis does not begin at zero or its differences are exaggerated. Also, examine the graph to determine whether objects or of area or volume are used for data that are actually one-dimensional only, so that the differences don't look exaggerated.
An internet provider occasionally conducts online polls in which users can respond to a question. If a graph is conducted, constructed to illustrate results from such a poll, and the graph is designed objectively with sound graphing techniques, does the graph provide information about the larger population of internet service provider users? Why or why not? Users can respond is the key note here. This is voluntary. So, the poll responders may not be representing the entire population. It's those who actually choose to respond to the survey. And those are examples of bad graphs.