Outliers and Misleading Graphs!

Statistics Unit: Week 2

Hello, all! We had only one lesson this week in Math 252, considering this previous Monday was a lab day, so this post will be on the short side.

Part 1: Outliers

By definition, an outlier is a "data point on a graph or in a set of results that is much bigger or smaller than the next nearest data point." That being said, while outliers may sound pretty obvious and easy to find, there is an equation that goes along with it. This is found by calculating/finding what is called the interquartile range (IQR), which is the distance between the quartiles.

The equation is simple enough: you subtract the upper quartile from the lower quartile, followed by multiplying that difference by 1.5.

An example would look like this:

Upper Quartile = 30, Lower Quartile = 23

First, subtract the upper quartile from the lower quartile to get the IQR:

30 - 23 = 7 --> IQR

You would then multiply the IQR by 1.5, like this:

7 x 1.5 = 10.5

Then, you would take this number to find the range of the outliers:

30 + 10.5 = 40.5 --> An outlier would be ABOVE 40.5

23 - 45 = -22 --> An outlier would be BELOW -22

** REMEMBER! An outlier is NOT just some random number on a graph/plot, or the biggest or smallest number you see when looking at a set of data. An outlier is found in a specific range and can only be done by following the equation steps above.

Part 2: Misconstrued Graphs/Data

In class this past week, we also learned of how graphs and statistics can sometimes misleading. This happens for a number of reasons from the graph having no labels, the distance between intervals being uneven, et cetera. Why this happens also has many reasons, but the main one being that those who construct the graphs only want the audience to see a certain perspective.

An example of a misconstrued graph would look like this:

The graph is made to show the difference in tax rate from now to early 2013. While the difference seems large and staggering, if someone were to look closely at this graph they would see that the difference is actually not that big. The "now" shows a 35% tax rate, while "2013" shows a rate of 39.6%. That is only a 4.6% increase, despite the graph depicting it to be much larger.

This is done by the scale of the graph. If you look at the scale to the right of graph, you will see that it starts at 34 (instead of 0) and ends at 42 - this makes it look as though there is huuuuuge difference because 35 is closer to the bottom and 39 is closer to the top.

While it is easy to miss these small details, it is also just as easy to fix. To make this graph more accurate, all you would have to do is readjust the scale (perhaps starting at 0 and ending at 50), so that it would show that the difference in tax rate is not that big.

Closing

Next week's blog post will center around the presentations in class, as well as the review homework we were assigned. Until next time!