For example, in the Greco-Roman civilization, the standard deviation was used to determine whether or not the results of a measurement were consistent or not. If there were deviations from the mean, the result should be considered inconsistent.
In ancient Greece, the standard deviation was used as a method to evaluate the ability of the person on the street to make predictions and decisions. Standard deviation would also be used to evaluate statistical procedures such as binomial sampling. Thus, it can be said that the standard deviation has been an essential part of human life for a very long time. And while this seems to make sense, it has been a mystery how standardized results come about, why they occur, and what factors can cause them.
According to some historians, the Greeks first realized the significance of standard deviation when they decided to determine the value of the circumference of the earth. With the help of mathematics, the Greeks discovered that the difference in areas of a circle and a sphere could be used to determine the area under a different latitudinal and vertical direction. In other words, the standard deviation was a way to measure the accuracy and precision of calculations. The discovery of standard deviation eventually led to the invention of the Greek alphabet.
In ancient Egypt, the standard deviation was also used by the Egyptians to measure the probability of a certain event. For example, the probability of a particular event occurring multiplied by its standard deviation would give us an approximate idea of what the probability would be if it did occur. In general, standard deviation is used to determine the value of a random variable. If, for example, we want to determine the value of a random variable that would give us a prediction of what the temperature of the Earth will be during a specific day in a year, a standard deviation of about one tenth of a degree would be used. Of course, there are different types of random variables, and they will have different values, but the meaning is essentially the same, which is why they should be considered in a single number and not separated into different parts and components.
In ancient Greece, standardized results were also used to determine if a certain situation was likely to happen again or to predict the value of a particular variable in the future. For example, if you wanted to determine the probability that there is going to be rain in the near future, then you could look at the statistical results of different situations that were predicted to have rain, such as a person getting sick. If the same person had another sickness the next year, the results of these two scenarios would then provide the exact probability of whether or not there is going to be rain. In other words, it is the variation from the mean.
Another type of standard deviation, called mean deviation, is used when comparing two or more data sets. If one data set has a higher mean than the other, it can be considered a lower than average value and thus, it is not as important as the higher mean. This is why it is used in many cases to calculate the probability of something happening.
As you can see, there are many different types of standard deviations and they all have different uses. From weather predictions to financial projections, you can always use the standard deviation to give you the information you need to make better decisions.
