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- https://math.libretexts.org/Courses/Heartland_Community_College/HCC%3A_Introduction_to_Statistics_(Lathrop)/03%3A_Summarizing_Data/3.3%3A_Measures_of_the_Spread_of_the_DataAn important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more wid...An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean.
- https://math.libretexts.org/Courses/Coastline_College/Math_C160%3A_Introduction_to_Statistics_(Lee)/02%3A_Descriptive_Statistics/2.08%3A_Measures_of_the_Spread_of_the_DataAn important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more wid...An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean.
- https://math.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Claassen_and_Ikeda)/08%3A_Describing_Data/8.05%3A_Box_PlotsIn addition to the mean and median, which are measures of the "typical" or "middle" value, we also need a measure of how "spread out" or varied each data set is. There are several ways to measure thi...In addition to the mean and median, which are measures of the "typical" or "middle" value, we also need a measure of how "spread out" or varied each data set is. There are several ways to measure this "spread" of the data.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_For_Liberal_Art_Students_2e_(Diaz)/09%3A_Statistics_Describing_Data/9.04%3A_Measures_of_VariationThere are several ways to measure the “spread” of a data set. The first is the simplest and is called the range. The range is the difference between the maximum value and the minimum value of the data...There are several ways to measure the “spread” of a data set. The first is the simplest and is called the range. The range is the difference between the maximum value and the minimum value of the data set. A more sophisticated measure of variation is called standard deviation. The standard deviation is a measure of variation based on measuring the distance each data value deviates, or is different, from the mean.
- https://math.libretexts.org/Courses/University_of_St._Thomas/Math_101%3A_Finite_Mathematics/03%3A_Probability_Distributions_and_Statistics/3.02%3A_Probability_Distributions_for_Discrete_Random_VariablesThe probability distribution of a discrete random variable X is a list of each possible value of X together with the probability that X takes that value in one trial of the experiment. The proba...The probability distribution of a discrete random variable X is a list of each possible value of X together with the probability that X takes that value in one trial of the experiment. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P(x) must be between 0 and 1 and the sum of all the probabilities is 1 .
- https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/10%3A_Descriptive_Statistics/10.12%3A_Measures_of_VariationIn addition to the mean and median, which are measures of the "typical" or "middle" value, we also need a measure of how "spread out" or varied each data set is. There are several ways to measure thi...In addition to the mean and median, which are measures of the "typical" or "middle" value, we also need a measure of how "spread out" or varied each data set is. There are several ways to measure this "spread" of the data.
- https://math.libretexts.org/Courses/Mission_College/Math_10%3A_Elementary_Statistics_(Kravets)/02%3A_Descriptive_Statistics/2.08%3A_Measures_of_the_Spread_of_the_DataAn important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more wid...An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean.
- https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_Matthew.Lathrop@heartland.edu/Introduction_to_Statistics_(Lathrop)_OFFICIAL/03%3A_Summarizing_Data/3.3%3A_Measures_of_the_Spread_of_the_DataAn important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more wid...An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean.
- https://math.libretexts.org/Courses/Coastline_College/Math_C160%3A_Introduction_to_Statistics_(Tran)/02%3A_Descriptive_Statistics/2.08%3A_Measures_of_the_Spread_of_the_DataAn important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more wid...An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean.
- https://math.libretexts.org/Courses/Mission_College/Math_10%3A_Elementary_Statistics_(Sklar)/04%3A_Discrete_Random_Variables/4.02%3A_Mean_or_Expected_Value_and_Standard_DeviationThe expected value is often referred to as the "long-term" average or mean. This means that over the long term of doing an experiment over and over, you would expect this average. This “long-term aver...The expected value is often referred to as the "long-term" average or mean. This means that over the long term of doing an experiment over and over, you would expect this average. This “long-term average” is known as the mean or expected value of the experiment and is denoted by the Greek letter μμ . In other words, after conducting many trials of an experiment, you would expect this average value.
- https://math.libretexts.org/Courses/Las_Positas_College/Math_for_Liberal_Arts/14%3A_Descriptive_Statistics/14.03%3A_Measures_of_Dispersion[1] The reason we do this is highly technical, but we can see how it might be useful by considering the case of a small sample from a population that contains an outlier, which would increase the aver...[1] The reason we do this is highly technical, but we can see how it might be useful by considering the case of a small sample from a population that contains an outlier, which would increase the average deviation: the outlier very likely won't be included in the sample, so the mean deviation of the sample would underestimate the mean deviation of the population; thus we divide by a slightly smaller number to get a slightly bigger average deviation.