I’m sorry I’ve been neglecting my blogging post of late – I’m in the midst of two summer classes at the moment (Statistics and Macroeconomics) and since they’re only 5 weeks long, they are quite intensive, so unfortunately that’s where the majority of my free time goes. Though I guess that’s not exactly free. Good news though, I finished my Microeconomics summer class and received an A in it 😀 Let’s hope I do just as good this session!
I decided I wanted to try theoretically killing two birds with one stone today, so this blog post may be relatively boring for some of you (hopefully not all). I have a statistics exam tomorrow and I need to study. However, instead of doing the run of the mill study routine, I thought I would turn it into an academic blog post. The exam is on the beginning material of the class, so don’t worry, it’s not incredibly intense. Also I won’t be insulted if you skip over this, but I think it’s at least worth giving a quick looksie 😉
OK. SO STATISTICS:
First, statistics is the embodiment of principles and methods concerned with extracting useful information from data; it is a descriptive measure or characteristic of the sample. It’s important, and it is used all the time, everyday, to help keep the wheel of our society spinning. I bet you can think of at least one example.
There are two different basic areas of statistics – descriptive and inferential. Descriptive statistics deals with methods of organizing, summarizing and presenting data such as describing shape, the average value or a spread of data. In descriptive, you have all the information already and no inferences are made. Descriptive stats are things like graphs, charts and tables. Then, there is inferential stats, which is a body of methods for drawing conclusions about a population based on information available in a sample taken from that particular population. We do this because a population can be so large that we cannot measure it in its entirety. When we gather our information for inferential stats, we generally use simple random sampling, which basically means each item of a population is equally likely to be chosen, there is no predisposition/bias. Other samplings exists, such as systematic, cluster, stratified and multistage.
Now let’s move into data, the information that is obtained by observing values of a variable. There are two types of data – quantitative and qualitative. Qualitative is simple enough; it is non-numerical, categorical or nominal. You list the distinct values and their frequencies and then divide the frequency by the total number of observations to get the relative frequency distribution. Then, there is quantitative data, which is numerical and where the variables are broken down into either discrete (whose possible values can be listed even though the list may continue infinitely) or continuous (whose possible values form some interval of numbers and usually deals with decimal points). For qualitative data, we look at frequencies or “counts”, where in quantitative we look at means and standard deviations. Which leads me to my next point…
Descriptive measures in stats are measures of central location, which are the mean (average), median (middle of data), and mode (most frequently occurring). If the distribution is symmetrical, the mean will equal the median. Then there are measure of variation, which are range (distance between minimum and maximum), sample standard deviation (measures the extent to which values differ from the mean) and the inter-quartile range (the third quartile minus the first, which is a range of the middle 50% of the data). There is also something called the five number summary, which includes the first, second and third quartile, along with the minimum and maximum.
I want to talk about standardized variables, z-scores and how to actually obtain the standard deviation, but I think that’s maybe for another day. Or maybe never for this particular blog. Either way, enjoy the rest of your summer Sunday! x’s and o’s.