Do you know what variance is? Don’t worry, I did the research for you, I’ll do my best to explain it to you correctly. I invite you to learn together.
Mathematics is full of analysis, equations and formulas for infinite calculations. We can find it in all fields and branches of the study of humanity.
Today I not only want you to know what variance means but also to be able to do analysis of variance. You will discover many things after learning about the analysis of variance and it will help you to know how to calculate it.
I want to show you formulas or equations that can help you determine values, and discover where the famous variance appears from. Always keep in mind that the variance is the value of an exact measure or not squared. I will try to make you understand all this as clearly as possible. I want to show you without going to mathematical terms that may be very difficult for you to understand.
This study requires a lot of analysis and attention, if you miss something, please go back to the beginning. Do not be left with doubts and if necessary make your own calculations.
Theory of Probabilities and Hope
In the study of mathematics we can find dissimilar concepts. Among them we find the much heard theory of probability. This is the one in charge of the study of phenomena often found, this is where we can say that two plus two are not always four. This theory gives us the possibility of having an approximate calculation of a probable result. At the moment physics and economics work together with this theory.
In mathematics you will often hear a term called hope. In other circumstances this word would be familiar to you as a result of the meaning it has in other branches. I tell you that the meaning is the same for mathematics. We have hope when we expect an absolute value for a mathematical operation. Hope is represented in mathematics by the letter “E”.
Among one of the many things that we find in mathematics, we are going to see today something called variance. The variance is represented as: V and many times also as an “o” squared. Among the variances we find the sample variance and the covariance.
Variance
I will tell you that the variance is a scattered unit of measurement, we find this as the expectation in a squared calculation before another unit of measurement.
Example: if you have a room where two of its walls measure three meters and the other two measure two meters, we multiply the one wall of three meters by one of two meters. The calculation is three times two and we square this operation, the variance is six square meters, so you know that you have a room of six square meters. Like almost all units of measurement, the variance has an initial value of zero.
If a calculation has no hope, it is impossible to obtain its variance. We also find operations that despite having hope do not have variance. When you see in a calculation a letter “o” raised to the square, it is the representation of the variance. Variance is used in almost everything related to mathematics. In quantitative genetics we can also find the analysis of variance. When we have a measure and it does not show us a distributed data form, we then need to find its variance.
Variance Calculation
One of the most complete examples when calculating the variance are the dice. These have six faces, we can say that their value is from one to six. To know its variance, we must first decompose these six faces as: (1+2+3+4+5+6)/6 = 3.5.
3.5 2 ₌ {2.5} 2 + {-1.5} 2 + {-0.5} 2 + 0.5 2 + 1.5 2 + 2.5 2 } ₌ . ₌17.50 ≈ 2.92
With this equation we can then determine that the variance for a six-sided dice is 2.92. We then say that the six faces of the dice is the variable, when breaking it down we find the value and that through the equation we obtain the variance.
Sample Variance
To determine the sample variance there are three fundamental calculations or formulas. One of them is found through geometry, the calculation of averages of a pair of data or also the average of the differences of the data.
Covaraince
This is in charge of indicating the variation according to the measurements. When the values of a variable are equal to the values of another variable, we are in the presence of a favorable or positive covariance. When the values of a variable are greater than those of a variable with smaller values, it is called a negative variable. The covariance is represented as: Cov. The covariance demonstrates the difference or not between the variables through its formulas.
Variance Analysis
Analysis of variance is well known and used in statistics. This analysis consists of determining differences. The analysis of variance is represented as ANOVA.
To determine this analysis it is necessary to use specific formulas for this case. In these formulas the values are decomposed and calculated.
There is a table for the analysis of variance, this is applicable once the calculation has been made. This is called the analysis table. In it we find: sources of variation, sum of squares, degrees of freedom, mean square and F. This table is divided into intergroups, intragroup or error and total value. In statistics the “F” is the way of distributing the probability.
Within this analysis we also find the multivariate analysis, this term is identified as MANOVA. This is based on combining values that cannot be easily combined. It is also able to identify changes in dependent variables from independent variables.
One of the cases where the analysis of variance is most used is when calculating the population of a country. First, they calculate the sample measure through the decomposition of the values and then proceed to the squared calculation to obtain the variance.
Inflation factor
Statistics indicate that inflation is responsible for demonstrating that the variance of a coefficient increases and demonstrates its causes. According to one of its formulas, it is demonstrated that the separation of data provides a greater variance when estimating coefficients. A larger size value shows a smaller variance before a coefficient.
Unbiased Estimator
When we are in the presence of the value of a parameter, the estimator is the one with the lowest variance in relation to any other estimator. Example: when we have a distribution of measures and a variance that we do not know, the value and variance of the measure is the unbiased estimator.
Because all of this?
It is impossible for me to talk to you about variance without showing you everything that it entails and all the operations and requirements of which the analysis of variance consists. We can conclude by saying that the variance and its analysis consist of determining the variation in measurements of a value, this value once discovered is raised to the square.
It is a pleasure for me to be able to show you below the science in which variance is studied and practiced. This science is very old and is present in man from his birth to the end of his days, “mathematics.”
Can you imagine your life without mathematics?
History of variance in mathematics
This is the science that investigates the beginning, discovery and all factors in mathematics. In primitive times, the lengths and sizes of things were already measured, although they did not yet know the numbers. They distinguished quantities or sizes as: large or small, a lot or a little. The primitives, as we all know, cultivated, fished and even traded. Their products began to grow and they began to trade, among themselves and among other tribes. It was no longer enough to say it’s a lot, at that moment they began to count and name the numbers.
I tell you that at this time women already knew the days when they would have their menstruation. These days were represented with symbols inscribed in animal bone, they marked the twenty-eight or thirty days for the presence of their cycle. They did not know numbers but were governed by symbols.
It is said that mathematics began to be used in its beginnings as a necessity to market, to know the earth as a planet, dedicating calculations to the study of its measurements, even for knowledge of actions in space that until then had not been called astronomy.