The expectation of normal distribution is expressed by the mathematical symbol ξ, so the expectation formula of normal distribution is: e ξ = x1p1+x2p2+…+xnpn, and the variance is expressed by the mathematical symbol s, so the variance formula of normal distribution is: s =1/n [(x655

The normal curve is bell-shaped, with low ends and high middle, which is symmetrical left and right, so people often call it bell-shaped curve.

If the random variable X obeys the normal distribution with a mathematical expectation of μ and a variance of σ 2, it is recorded as N(μ, σ 2). The expected value μ of probability density function with normal distribution determines its position, and its standard deviation σ determines its distribution amplitude. When μ = 0 and σ = 1, the normal distribution is standard normal distribution.

Difference:

The average value of the sum of squares of the difference between the data in the sample and the sample average value is the sample variance; The arithmetic square root of the sample variance is the sample standard deviation. Sample variance and sample standard deviation are both measures of sample fluctuation. The greater the sample variance or standard deviation, the greater the fluctuation of sample data.

Variance and standard deviation are the most important and commonly used indicators to measure the discrete trend, and are the most important methods to measure the discrete degree of numerical data. The standard deviation is the arithmetic square root of variance, expressed by S.