Today we bring to the debate an apparently complex question, which for generations has confused both students and professionals, which encompasses a fundamental concept for our times, and has left more than one head hairless per year, dare to affirm a large part of the disciples during their course in the faculty. A question that for a change can lead to a fairly simple answer, it all depends on how you look at the problem. As we know that you are wanting to know the question that has created so much expectation, we simply write it to you, without further ado: What is a variance in statistics?
Statistical Variance?
If you are over eighteen years old, after reading this question your body will surely experience several types of reactions, an instantaneous reaction, which is nothing more than surprise mixed with a tingling that is desperate but controllable. Especially if you have ever had to answer how to calculate the variance.
Today we propose a practical analysis that will help you understand what variance is but in statistics, which will be very useful in life, at the same time it will free you from Alopecia.
History of variance and its concept.
We must thank Ronald Ficher for the term variance, who in a publication in 1918 proposed the variance as “the median of the deviations of a variable, if the mean value of said variable is considered.”
Seen in another way, the variance is a measure of dispersion that reflects, gives value to variations, deviations, assumes and accounts for what in some way could be defined as a possible margin of error.
What tends to confuse the most is that in probability theory, variance is understood as the Expectation of the square of the deviation of a variable from its mean, and although the term Expectation, used in a mathematical concept, is already in itself quite unusual, that is not to say that hope is calculable. I’m sure you’ve never heard anyone say, “I have 16.9 hopes you’ll kiss me” when picking a flower.
The most important thing to appreciate to understand this concept is that contrary to basic mathematics, and the conventional calculations that you have faced up to now, the probabilities are based on the calculation, the most exact possible of the prediction of some event.
Seen in another way, we have that the mathematics that you have studied up to now is based on facts, events and real objects, which exist in the present or were in the past, but which have already taken place and therefore it was possible at the time, to have a exact dimension of the object or phenomenon to be studied, which makes them perfectly quantifiable. However, the theory of probabilities proposes us to think about the future, and here we launch a new question, do you know what will happen tomorrow?
How can we predict the error?
Since its emergence and evolution, the world has followed a cyclical, constant and periodic development, and although we are referring to the natural world, to plants, rocks, fauna, it should be understood that we are not exempt from it, and the easiest proof is that you look right now at your left wrist and realize that your day, and your whole life, is based on small cycles of sixty minutes, which are constantly repeated one after the other.
This is why, based on history, in the meticulous analysis of each of these cycles, we have been able to draw different models or mathematical equations, which allow us in some way to have a notion, not of the future in general, but of a specific future event, which we will be able to calculate before it happens, depending on how good we are at analyzing probabilities.
The fact that we intend to quantify or define a future event frames the idea that said event can be exactly as we expect or similar, with some variations, and that is where variance comes into play, although in order to understand it better We still have to assess other concepts.
A very important concept when it comes to understanding variance is the standard deviation or typical deviation, which represents the magnitude of the dispersion of variables within the interval and ratio, but since this concept may be a bit abstract, let’s do it a little more. digestible.
An example to understand Statistical Variance
You intend to carry out a statistical analysis where you will assess the possibility that your father will give you a Mercedes. For this, the condition is that you must graduate with a gold diploma, and for this, apart from studying a lot, you must achieve an accumulated average that behaves in the range established for obtaining said title.
As you are a very cautious person and at the same time an excellent student, you ask yourself three unknowns and write them down on a piece of paper.
- How much do I have to accumulate to graduate with a gold diploma?
- What will be the standard deviation for the expected result?
- What will the variance be?
The first thing you will do is calculate the cumulative result of your grades so far, and there you will know your average, or what is the same, the average of your evaluations.
Then you must make an analysis of how many points you must raise or maintain to reach the expected value, which will force you to focus on some subjects and others not so much, with the purpose of obtaining your goal, the gold diploma that “El Mercedes” will guarantee.
To guarantee the diploma you must end up with a school average that fluctuates between a minimum value and a maximum value, which if we hypothetically quantify them can be 10 points of maximum value and 9.5 of minimum value.
Applying Statistics
Therefore, you should prepare to end up with an average cumulative of 9.75 points, which will be your expected result from now on, however, if you end up with any other average that is in the range between 10 and 9.5, such as 9.6, you also get the diploma even if your result is similar, but not the same as expected.
If we apply the statistics to the above, we have that you must achieve an expected value of 9.75 points in your grades, with a standard or typical deviation of between 0.25 points that will guarantee the result you want, and the variance will be equal to your standard deviation raised to the square, since what the variance does is establish the variability of the random variable.
Not so abstract concept
If after having done this reasoning you still want to straighten your hair, you should consider two possibilities:
- Do not be upset or cause your father more worries, take your life by the hand and be considerate, even if it is painful for you, change the “Mercedes” for a scooter and go out into the street, you will see how you find countless possibilities to open up step in life A universe that doesn’t require you to calculate the variance, or the mean, or the standard deviation, be happy.
- If even with your hair straight you feel that you can, and above all you want to continue trying to understand these concepts, go ahead! Nothing has been written about cowards. To face this and other much more abstract concepts, you just have to put a lot of effort and dedication, remember if others can too.
Of course, if you opt for this second option, it does not hurt to have a hair treatment from time to time, to avoid possible aesthetic damage.