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Frequency: the number of times a value of the data occurs. Relative Frequency: the ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes. The number of times a value of the data occurs is called absolute frequency.So relative frequency isContinue reading “Relative frequency and its properties”

From the representation of the information in the form of a database table (data matrix) to analyze some aspects of the variables under examination, a distribution of the frequency is necessary. Any process of data synthesis causes loss of information. For example, on a distribution of individuals with a height between 140 and 170 cmContinue reading “Loss of information and gain for interpretation”

The scale of measurement is a logical tool through which it is possibile measure a statistical unit. There are two types of scale of measurement: For a qualitative variable: • nominal scale: differentiates between items based only on their names and other qualitative classifications they belong to, characterized by a absence of pre-established order. HairContinue reading “Scale of measurement”

The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled. Therefore, if a population has a mean μ, then the mean of the sampling distribution of the mean is also μ. The symbol μM is used to refer to the mean of the samplingContinue reading “The sampling distribution of the 𝞵 and the 𝜎”

A measure of variability is a summary statistic that represents the amount of dispersion in a dataset. How spread out are the values? While a measure of central tendency describes the typical value, measures of variability define how far away the data points tend to fall from the center. We talk about variability in theContinue reading “Dispersion”

A moving average is a technique to get an overall idea of the trends in a data set; it is an avarage of any subset of numbers. The moving average is extremely useful for forecasting long-term trends. You can calculate it for any period of time. For example, if you have sales data for aContinue reading “Running mean”

Here we can define, 2 events: A and B. If the occurrence of event A doesn’t affect the occurrence of event B, these events are called independent events. In this case the probability of P (A ꓵ B) = P (A) * P (B). If are dependent events we can define: event A is the probabilityContinue reading “Bayes Theorem”

Boole inequality and calculation of union probability of n arbitrary events: In probability theory, Boole’s inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. Formally, forContinue reading “Boole’s inequality”

The concept of probability has more definition: classic probability, frequentist probability, and subjective probability. The classic probability is based on the hypothesis that all cases of the event are equally likely. It is define as the ratio between the number of favorable cases and the number of possible cases. The frequentist probability is based onContinue reading “Definition of probability”

Kolmogorov axioms: An axiomatic approach is taken by Kolmogorov to define probability. Let S denote as event space with a probability measure P defined over it, such that probability of any event E ∈ S is given by P(E). Then, the probability measure obeys the following axioms: Axiom 1: The probability of an event isContinue reading “Probability axioms”