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If the mean =, the first factor is 1, and the Fourier transform is, apart from a constant factor, a normal density on the frequency domain, with mean 0 and variance /. In particular, the standard normal distribution φ {\textstyle \varphi } is an eigenfunction of the Fourier transform.
Each standard deviation represents a fixed percentile. Thus, rounding to two decimal places, −3σ is the 0.13th percentile, −2σ the 2.28th percentile, −1σ the 15.87th percentile, 0σ the 50th percentile (both the mean and median of the distribution), +1σ the 84.13th percentile, +2σ the 97.72nd percentile, and +3σ the 99
A large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean. For example, each of the three populations {0, 0, 14, 14}, {0, 6, 8, 14} and {6, 6, 8, 8} has a mean of 7. Their standard deviations are 7, 5, and 1, respectively.
The arithmetic mean, or less precisely the average, of a list of n numbers x 1, x 2, . . . , x n is the sum of the numbers divided by n: + + +. The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition and division:
42 is a pronic number, [1] an abundant number [2] as well as a highly abundant number, [3] a practical number, [4] an admirable number, [5] and a Catalan number. [6]The 42-sided tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane.
The Richter scale [1] (/ ˈ r ɪ k t ər /), also called the Richter magnitude scale, Richter's magnitude scale, and the Gutenberg–Richter scale, [2] is a measure of the strength of earthquakes, developed by Charles Richter in collaboration with Beno Gutenberg, and presented in Richter's landmark 1935 paper, where he called it the "magnitude scale". [3]
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Mean maximum °C (°F) 5.0 (41.0) 6.3 (43.3) ... (26.6) 4.4 (39.8) Mean daily minimum °C (°F) −6.4 (20.5) ... (42.4) 2.2 (36.0) −3.5 (25.7) −8.3 (17.1)