"Gaussian distribution" is synonymous with the normal distribution, which is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valied random variables whose distributions are not known. A Gaussian distribution is defined by its mean (average) and variance (or equivalently, its standard deviation).
Here are some key properties of the Gaussian (normal) distribution:
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Symmetry: The distribution is symmetrical around the mean. This means that the left and right sides of the graph are mirror images of each other.
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Mean, Median, and Mode: For a normal distribution, the mean, median, and mode are all the same value, occurring at the center of the distribution.
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Bell Curve: The shape of the normal distribution is known as a "bell curve" because of its bell-like shape.
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Defined by Two Parameters: The exact shape of a normal distribution is defined by its mean (μ) and its standard deviation (σ). The mean determines the center of the distribution, and the standard deviation determines the spread.
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68-95-99.7 Rule: Approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This is also known as the empirical rule.
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Skewness and Kurtosis: The skewness of a normal distribution is zero, meaning there is no skew or bias to the left or right. The kurtosis is 3, which describes the "peakedness" of the distribution; a Gaussian distribution is mesokurtic.
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Probability Density Function (PDF): The formula for the normal distribution's probability density function includes a constant formed from π and e (the Euler number), the mean, and the standard deviation.
