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The mean, often referred to as the average, is a measure of central tendency that is calculated by summing all the values in a dataset and dividing by the number of values. It provides a useful summary of the data but can be heavily influenced by outliers, making it less representative in skewed distributions.
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The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in order. It is particularly useful for skewed distributions as it is not affected by extreme values, unlike the mean.
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The mode is a statistical measure that identifies the most frequently occurring value in a data set, providing insight into the data's central tendency. It is especially useful for categorical data and can be used to highlight the most common category or value in a distribution, although it may not always be unique if multiple values occur with the same frequency.
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Variance is a statistical measure that quantifies the dispersion of a set of data points around their mean, providing insight into the degree of spread in the dataset. A higher variance indicates that the data points are more spread out from the mean, while a lower variance suggests they are closer to the mean.
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Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. A low Standard deviation indicates that the data points tend to be close to the mean, while a high Standard deviation indicates a wider spread around the mean.
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In mathematics, the range of a function is the set of all possible output values it can produce, based on its domain. Understanding the range is crucial for determining the behavior of functions and their applicability to real-world scenarios.
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The interquartile range (IQR) measures the Spread of the middle 50% of a dataset, providing a robust indicator of variability that is less influenced by outliers. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3), offering insight into the distribution's central tendency and dispersion.
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Percentiles are statistical measures that indicate the relative standing of a data point within a dataset by dividing it into 100 equal parts. They are commonly used to understand the distribution of data and to identify where a particular value falls in relation to the rest of the dataset.
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Skewness is a statistical measure that describes the asymmetry of a probability distribution around its mean. It helps in understanding whether data points are skewed to the left (negative skewness) or right (positive skewness), indicating the direction of outliers and potential biases in data analysis.
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Kurtosis is a statistical measure that describes the shape of a distribution's tails in relation to its overall shape, indicating the presence of outliers. It helps in understanding whether a dataset has heavier or lighter tails compared to a normal distribution, with higher kurtosis signifying more outliers and potential extreme values.
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Effective value, often referred to as root mean square (RMS) value, is a statistical measure of the magnitude of a varying quantity and is used extensively in electrical engineering to quantify the equivalent DC value of an AC waveform. It provides a consistent method for comparing the power delivered by different waveforms, ensuring accurate and reliable calculations in power systems and signal processing.
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Mean deviation, also known as average absolute deviation, is a measure of statistical dispersion that quantifies the average distance between each data point and the mean of the data set. Unlike variance or standard deviation, Mean deviation uses absolute values, making it less sensitive to outliers and providing a straightforward interpretation of variability.
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The Gini Coefficient is a statistical measure of income or wealth distribution within a population, ranging from 0 to 1, where 0 represents perfect equality and 1 indicates maximal inequality. It is widely used in economics to assess inequality levels and track changes over time, offering insights into social and economic policies' impacts.
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