Presentations

Today in class we watched the presentations and had a review day. The common theme was "Mean, Median and Mode", but it was helpful to see the concept presented in multiple different ways. One way that that really "clicked" with me, was Hayley's presentation with the marshmallows. The main idea of this was to realize that you can really see the data a lot better if you put it into a visual (in this case, that was the marshmallows for a dot plot). This helps you to understand what the data is really telling you.

Just as a visual, here is a set of data and a graph concerning heights:

The graph is WAY more visually appealing than the data table and really let's you know a lot more about the dat just by looking at it!


Another presentation that left an impact was one that talked about the WHY behind using mean, median and mode.

I had never really thought about why you would need to use one over the other in certain situations, I always just found out all three because I was told to, or the mean because it is most commonly used.

That presentation got me thinking about how outliers can really affect your number, and finding the median would be more appropriate in situations where there are outliers because they would make the mean a little off, and therefore it would not be as effective of an indicator of the data.

Box and Whisker Plots

Box and Whisker plots are used as a way to display a set of data.  There are a lot of things you can tell about the data, by just looking at the graph. For instance, you know the range that the data falls within, and the median just from the first glance!

Here is what a box and whisker plot looks like:

There's a lot of information on here, but what does it all mean? 

Lower Quartile and Upper Quartile can be kind of confusing. 

Lower Quartile is the median of the lower half of the data set

and...

Upper Quartile is the median of the upper half of the data set 

Box and whisker plots are kind of unique, but they have many different real-life applications, such as...

• You can use them to compare different sets of data.
• You could use it to compare the heights of students in a classroom (I believe we did this in class).
• It would be a great way to look at test scores and see where the majority of the scores lie. 

Standard Deviation

Yesterday in class we learned about standard deviation. This is something that I had learned about in my AP Stats class in high school but because it's a really confusing concept, it was a good refresher.

The basic standard deviation equation is:

SEE IT'S CONFUSING. 

If this was your first reaction too, it's okay. It's much easier when you break it down, I promise! 

I find it's easier if you think about the concepts of the equation (i.e. WHAT does this equation tell us to do?)

Step 1: To find standard deviation you start by finding the average of your set of numbers. I'm sure most people know how to find the average, but it's found by adding up all of the numbers and then dividing that sum by how many numbers there are.

After you've found the average, you can start using the equation.

Step 2: To find SD (that's standard deviation, I like to abrev), you take each individual number in your set of data and subtract it from the mean. Then you square that number. You do this for each number in your set of data and add them together.


Ex: If your average is 10, and your data contains: 15, 12, 14, 11

(10-15)^2 + (10-12)^2 + (10-14)^2 + (10-11)^2


Step 3: Next, you divide the number you found in Step 2, by how many numbers there are and subtract one.

Ex: Using our example from above. There are four numbers so we would divide by (4-1).

Step 4: Once you have your number you need to find the square root of that and then, you've found the standard deviation!

But what did you actually just find?

Well, the standard deviation shows you how much the data deviates away from the mean.

• 68% of the data lies within one standard deviation of the mean. 
• 95% of the data lies within two standard deviations of the mean. 
• 99.7% of the data lies within three standard deviations of the mean. 

Once you understand the equation for standard deviation and what all the symbols mean, you can find out a lot of information from looking at a bell curve like the one above. Understanding standard deviation is a great asset because it allows you to interpret data, and bell curves are a type of graph you will encounter throughout your life, especially as educators!