Variance Schmariance....1512

I don't think I've been this frustrated in a long time! I knew that things wouldn't stay easy for long in this class but I did not expect to get hung up like I was when I came upon calculating variance! I don't know how many times I worked these problems over in the homework and practiced them out of the book. I also followed examples and step-by-step instructions in the homework assignments, but I still could never come out with the right answer. Finally, I realized I had to take a deep breath, take a break, and come back to it.

When I finally came back to variance, I decided that the first thing I needed to do was SLOW DOWN. Then I needed to take each step one at a time and make sure that all the numbers I was plugging in were right and that I was completing each part of the steps. Once I slowed down and stopped panicking, I was able to think and calculate better (thank goodness!).

The definition of variance and how to find it is what threw me off. This can seem a little daunting:
(S^2) = summation[( x - mean)^2] / n-1

In easier terms, variance is computed as the average squared deviation of each number from its mean.

First, find the mean of the set of numbers you have.
Then, subtract the mean you calculated from each number in the set.
Now, square each number that you have come up with.
Finally, add those squared numbers together and divide them by the amount of numbers that existed in the original set.


For instance, for the numbers 1, 2, and 3, the mean is 2 and the variance found this way:



If this isn't helpful or you're still confused, you can watch this video. It was helpful for me! I can do this with or without a calculator, and the video show to use one, but you obviously don't have to. I think it's a good idea to do it without for the sake of becoming less dependent on them. This is doable! The following site was also great!

Variance and Standard Deviation Site

Unions and Intersections of Sets - 1510

When I was in school, math was not my favorite subject and I seem to remember very little other than the basics and for anything difficult or unfamiliar I turn to a calculator or the Internet to help me. So far this class (1512) has not thrown anything at me that I wasn't able to figure out without a refresher, until now, that is. This week, I ran into some problems when our section began discussing sets, specifically when it came to unions and intersections of sets. I remember disliking this stuff back in high school and I cringed when I had to start doing it this week.

The chapter that I read did a good job of explaining sets, and what an intersection or a union is, but when I went to work on the homework problems I kept forgetting which was which and would find myself referring back to the book again. I know it sounds silly, but I finally realized something that will hopefully help me remember the difference between the two:

The U is the union and it's like a marriage - everything comes together and becomes one. The intersection is just like a traffic intersection - the roads that each car is on are separate, but the place in the middle where all the roads become ONE is the intersection, and that's the same with the sets. The intersection includes the elements that are in common.

I also found that Venn diagrams are helpful to me in understanding this concept. I am a visual learner and I really found it helpful to look at the idea of a union and an intersection, and it was even more helpful to create a few of my own. Also, the video below was also helpful and I think it would be helpful for a younger student that may not being grasping the concept.

Now that I've gone through this stuff, the unions and intersections of sets aren't as daunting or as confusing to me anymore. I hope that if you had any issues with this concept, this blog has helped you in some way to understand!

First Time Blogging!

Today I set out to create my very first blog account and I have done it! I am really happy with the way it has turned out and I can't wait to start writing my first posts related to elementary mathematics. I look forward to a fun and informative semester of learning how to teach math!