What is the variance formula and what is the formula for variance

The variance is the expected value of the square of the difference between the actual value and the expected value, whereas the standard deviation is the square root of the variance. In the actual calculation, we calculate the variance with the following formula. The variance is the mean of the squares of the difference between the individual data and the mean, i.e., s 2=(1 n)[(x1-x) 2+(x2-x) 2+.

xn-x ) 2], where x is the mean of the samples, n is the number of samples, 2 is the square, xn is the individual, and s 2 is the variance. And when using (1 n)[(x1-x) 2+(x2-x) 2+.xn-x ) 2] as an estimate of the variance of the population x, it is found that the mathematical expectation is not the variance of x, but (n-1) n times the variance of x, [1 (n-1)][x1-x ) 2+(x2-x) 2+...

The mathematical expectation of xn-x ) 2] is the variance of x, and it is "unbiased" to be used as an estimate of the variance of x, so we always use [1 (n-1)] xi-x ) 2 to estimate the variance of x, and call it "sample variance". Variance, in layman's terms, is the degree of deviation from the center! It is used to measure the fluctuation of a batch of data (i.e., the amount by which the batch deviates from the average).

In the case of the same sample size, the larger the variance, the greater the fluctuation and the more unstable the data.

It is the sum of squares obtained by subtracting the average of their totals.

What is the formula for calculating the variance of a constant?

s square = (x1-x pull) (x2-x pull) (x3-x pull) -xn-x pull) n x pull is the average.

Variance: The mean of the sum of squares of the difference between individual data and the mean in a set of data.

The average is: (3+4+5) 3=4.

The variance is: 1 3*[(3-4) 2+(4-4) 2+(5-4) 2]=1 3*(1+0+1)=2 3.

The latter parameter of the normal distribution reflects the degree of its deviation from the mean, i.e., the degree of fluctuation (random fluctuation), which is consistent with the characteristics of the graph.

Solution: According to the distribution law given in Example 2 in the previous section, it is calculated that the number of waste products of worker B is small, the fluctuation is small, and the stability is good.

1. Let c be a constant, then d(c) = 0 (the constant does not fluctuate).

2. d(cx)=c2d(x) constant squared extraction, c is a constant, x is a random variable); Evidence: In particular, d(-x) = d(x), d(-2x) = 4d(x) (no negative variance).

3. If x and y are independent of each other, then it is proved that the first two items are d(x) and d(y), and the third term is when x and y are independent of each other, so the third term is zero.

There are two formulas for calculating variance: Method 1: s 2=1 n [(x1-x) 2+(x2-x) 2+

xn-x) 2] The first x is the number of data, and the last x is the average of this set of data, and x1, x2, xn, etc. are the second method of each data: s 2=1 n (x1 2+x2 2++xn 2)-x 2 standard deviation is the square root of the variance, i.e.: s= 1 x [(x1-x) 2+(x2-x) 2+

What is the formula for calculating the variance of a constant?

1. If x1, x2, x3...The average of xn.

is m, then the variance formula of the mu band.

It can be expressed as: <>

2. The formula for standard deviation.

The values in the formula are x1, x2, x3 ,..xn (all real numbers) and its average (arithmetic mean.

is , and the standard deviation is .

Nature of variance:

When the data distribution is scattered (that is, the data fluctuates greatly around the mean), the sum of squares of the difference between each data and the mean is larger, and the variance is larger. When the data distribution is compared to the set, the sum of squares of the difference between each data and the mean is smaller. Therefore, the greater the variance, the greater the fluctuation of the data; The smaller the variance, the less volatile the data will be.

The mean of the sum of the squares of the difference between each data in the sample and the sample mean is called the sample variance; The arithmetic square root of the sample variance.

This is called the sample standard deviation. Sample variance and sample standard deviation are both measures of the size of a sample's fluctuation, and the larger the sample variance or sample standard deviation, the greater the fluctuation in the sample data.

Variance is calculated by the formula:

Set a set of data x1, x2, x3 ......In xn, the squares of the difference between each set of data and their mean x are (x1-x)2, (x2-x)2, and ......, respectively(xn-x)2, then it can be measured by their average by the formula:

This formula is mainly used to measure the fluctuation of this set of data, and it is called the variance of this set of data. For the sake of brevity, we can also write it down:

If the variance of a set of data is smaller, then it proves that the stability of the group of data is higher.

Common variance formulas:

1) Let c be a constant, then d(c)=0.

2) Let x be a random variable and c be a constant, then there is d(cx) = (c)d(x).

3) Let x and y be two random variables, then: d(x+y)=d(x)+d(y)+2e.

In particular, when x and y are two random variables that are independent of each other, and the third term on the right side of the above equation is 0 (common covariance), then d(x+y)=d(x)+d(y). This property can be generalized to the case of a limited number of independent random variables in the case of segment distress.

The formula for variance is s = (1 n)[(x1-x) x2-x) xn-x)

Variance is a measure of how much dispersion a random variable or set of data is measured by probability theory and statistical variance, and variance is used to measure the degree of deviation between a random variable and its mathematical expectation, the mean. The variance in statistics is also equal to the sample variance, which is the average of the square values of the difference between each sample value and the mean of the whole sample value. Talk about it.

The role of ANOVA:

In order to compare the means of more than two groups, the method of ANOVA can usually be used, which also includes BIBI, which means that ANOVA is used to test the significance of the difference between the means of two or more samples. In the quantitative analysis research in many fields, it is very important to find the important influencing factors among the many influencing factors.

For example, in agricultural production, we always want to get a higher crop product with as little input cost as possible. There are many factors that will affect the yield of crops, such as seed varieties, fertilization, climate, region, etc., which will have a greater or lesser impact on the yield of crops. If we can grasp which of the many influencing factors play a major and critical role in crop yield, we can control these key factors according to the actual situation.

The variance is the mean of the sum of the squares of the difference between the individual data and the mean, and the formula is:

If the average of x1, x2, x3, xn is m.

then the variance s 2=1 n((x1-m) 2+(x2-m) 2+.xn-m)^2）。

Variance, the mean of deviations from the square, is called the standard deviation or mean square deviation, and variance describes the degree of fluctuation.

Square difference: a -b = (a + b) (a-b). Literal expression: The product of the sum of two numbers and the difference between them is equal to the square difference of the two numbers. This is the squared difference chamber side formula.

Standard Deviation: Standard Deviation = sqrt(((x1-x) 2+(x2-x) 2+.xn-x)^2)/n)。

is the square root of the arithmetic mean from the square of the mean deviation, denoted by . In probability statistics, it is most commonly used as a measure of the degree of statistical distribution to make a circle simplification. The standard deviation is the arithmetic square root of the variance.

Standard deviation is a reflection of how discrete a dataset is.

The variance formula is shown in the figure below

Variance is defined differently in statistical descriptions and probabilistic hand scatters, and has different formulas.

In statistical descriptions, variance is used to calculate the difference between each variable (observation) and the population mean. In order to avoid the sum of the mean deviation from being zero, and the sum of squares of the mean deviation is affected by the sample content, the sum of the squares of the mean deviation is used to describe the degree of variation of the variables.

If the population obeys a normal distribution n( ,2), then (n-1)s 2 2 is slowly followed by a chi-square distribution with degrees of freedom n-1, so that d[(n-1)s 2 2] = 2(n-1).

If you give a few specific values, then find the mean first and then according to the formula: the variance is the mean of the squares of the difference between the individual data and the mean, i.e., s = (1 n)[(x1-x) x2-x ) xn-x ) where x is the mean of the samples, n is the number of samples, xn is the individual, and s is the variance.

As a function of a random variable, the sample variance is itself a random variable, and it is natural to study its distribution or modulus. In the case where YI is an independent observation from a normal distribution, Cochran's theorem states that S2 obeys a chi-square distribution: