Presentations & Study Guide Notes!

Statistics Unit: Week 3

For our final week in our Statistics unit, we focused on the presentations/lesson plans that were given in class, as well as the study guide assigned.

Part 1: Presentations

While all of the presentations were well thought-out and executed, they all focused on "Mean/Median/Mode" - this gave us little help with the other components that will be on the exam such as Standard Deviation, Outliers, and Box & Whisker plots.

That being said, there were a couple of presentations that stood out most to me:

1. Presentation #1 (Hailey): This presentation focused on finding the mean/median/mode of a large set of data by putting it into a dot plot. The data was based off the ages of the presenter's Facebook friends and, as such, there were several numbers that repeated multiple times. What stood out to me was that I struggled to add all 49 numbers and calculate the mean/median/mode in a strictly mathematical way. What I failed to realize until after was that I could have organized them into the dot plot FIRST. This would have made easier to find all three M's without doing as much work. Overall, I found this lesson helpful to me because it made me see that their are much easier ways to find answers to mathematical questions without listing out every single data point.
2. Presentation #3 (Kaycie): This was the presentation where we found mean/median/mode by using different color-coded candy. Many in class found this confusing and somewhat tricky, but I feel as though the point of the lesson was to show us that sometimes, we get tricked by multiple different factors. There was a large mix of candy (from Skittles, to M&Ms, to Mike&Ikes) and it confused people because they did not know whether to sort the groups by color or type of candy. While it seems trivial, this is an important concept because oftentimes in math exams or homework, we are given multiple variables in one problem. What is important is that we distinguish what is important information and what is not.
3. Presentation #6: The last presentation was also mean/median/mode, but was different from the other in that it incorporated the Box & Whiskers plot and outliers. This was a nice refresher because it reminded us how to create a Box & Whiskers plot, as well as calculate the positive and negative outliers by using the IQR equation.

Part 2: Study Guide

While I have not yet fully completed the study, there were two things that I found extremely useful/important to know for tomorrow's exam:

The 5-Number Summary: One of the problems in the study guide was to find what the 5-number summary was in a group of data and/or graph. I was unsure of what this meant until I looked it up and a 5-number summary is this:

Minimum - Lower Quartile - Median - Upper Quartile - Maximum

This summary is basically the main, definitive points in a Box & Whiskers Plot. This is important because a 5-number summary gives us the general range or extremes of the data set.

Bell Curve: Another thing I found to be important was the problems concerning the bell curve (Section 13.3, #11 A-C). This is especially tricky for me because I often confuse myself and make little mistakes when it comes to calculations. These problems helped reinforce my knowledge of the percentages that go into the bell curve (68%, 95%, 99.7%) as well as how to compute standard deviation when given a mean and an interval.

Outliers: The study guide also helped me practice with outliers, which I feel wasn't covered as much as I would've liked in class. If you want help on how to calculate the IQR and find the positive and negative outliers (if any), please refer to my second blog post below this.

Closing

I hope my blog has helped clarify some concepts we learned during this short Statistics unit in Math 252. I wish everyone good luck on the exam!

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!