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Guilherme Mazui

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What is the Difference Between Mean and Expectation?

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The difference between mean and expected value lies in the context in which they are used and the types of data they represent. Here are the key distinctions between the two:

  1. Context: Expected value is used when we want to calculate the mean of a probability distribution, representing the average value we expect to occur before collecting any data. In contrast, the mean is typically used when we want to calculate the average value of a given sample, representing the average value of raw data that we've already collected.
  2. Data Type: Expected value is related to probability distributions, which involve the probability that a random variable takes on certain values. Meanwhile, the mean is usually associated with finite sets of values, such as the average of a collection of numbers.

To summarize, the expected value is a measure of the average value expected from a probability distribution before collecting data, while the mean is the average value calculated from a given sample of raw data.

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  • What is the Difference Between Mean and Expectation?
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    • Comparative Table: Mean vs Expectation

    The difference between mean and expected value lies in their definitions and applications. Here's a summary of their differences:

    Mean Expected Value
    The mean is a measure of central tendency, representing the average value of a dataset. The expected value is a theoretical average, often referred to as the long-term average or mean, which represents the value you would expect to obtain over many trials of a statistical experiment.
    The mean is an empirical average of a sample of data, used for descriptive statistics. The expected value is a population concept, used to predict outcomes in probability theory and statistics.
    The mean is calculated by adding all the values in the dataset and dividing by the number of values. To find the expected value, you multiply each value of the random variable by its probability and sum the products.

    In summary, the mean is an empirical average based on actual data, while the expected value is a theoretical average that represents the long-term outcome of an experiment or event.

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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.