Statistics for Modern Life: 04 Learning to Sum

Robert RamstetterStarred Page By Robert Ramstetter, 27th May 2015 | Follow this author | RSS Feed | Short URL http://nut.bz/3p9xvpym/
Posted in Wikinut>Guides>Science>Numbers And Maths

Now that you have the data, what are you going to do with it? The first step is knowing how to add the variables.

The Sum is the most basic step in computing statistics

In the first three articles, you were introduced to some of the basic terminology and reasons for gathering statistics. Now that you have the data, what are you going to do with it? The first step is knowing how to add the variables. While your first thought may be that this is going to be simple, but summing is more complex than simple addition when you are dealing with statistics.
Do not be confused by the implied simplicity of this function. The SUM of X, for instance, is simply derived by adding the X variables together. However, it is not that simple when your equation employs brackets, squared variables, and square roots. A little common sense, though, will help you to understand the differences and permit you to arrive at the correct answer.

The Basic Sum Expression

The symbol for SUM is the Greek letter sigma. It is understood as denoting the summation of something. While this may seem easy at first, in order to arrive at the correct answer. The position of parenthesis, squared and square root symbols, and division lines will impact your answer. Below, I will demonstrate a few of the correct methods of summing a list of numbers.

Order of Operations

Notice how the placement of the square significantly impacts the order of your formula and arrives at a different answer. When you see the sigma, you must remember that your mathematical expression becomes multi-layered. Therefore, the sum of X squared will include more than one variable for "X" and, therefore, it will need to be treated differently.

The X,Y Axis for all your graphing needs:

Before we begin, I do not want to assume any prior knowledge from the reader. After all, if I am writing this to help explain basic concepts in Statistics, it would be foolish if I were to leave out the basic foundation and assume it to be understood. All graphs have a vertical and a horizontal axis. As you can see, the vertical axis is denoted as the “Y” axis, whereas the horizontal axis is denoted by the “X” axis. This is typical of practically all graphs. Understanding this will make reading graphs and plotting coordinates simple and, most importantly, accurate. If you have trouble remembering this, just think if the letter “Y”. the “Y” looks like a “V” with a tail at the bottom. If you associate the “Y” axis with the “V” in “Vertical”, you shouldn’t have a problem. Another point to remember is the “X” axis will generally be the variable, whereas the “Y” axis will be the results.
As you get deeper into plotting variables on a graph, there are two terms that you will need to know:
Predictor Variable: This is the X axis and it represents the variable that you are measuring and from which a prediction is made.
Criterion Variable: This is plotted on the Y axis. It represents the variable to be predicted, or the result of the Predictor Variable.


For more on statistics, see my main page:
Statistics for Modern Life: 01 An Introduction

Tags

Math, Mathematics, Sigma, Statistics, Sum

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author avatar Robert Ramstetter
Robert Ramstetter is a world traveler and writer of short stories, full length novels, and a vast array of technical articles.

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