What kind of results can the variance be calculated and obtained?

Variance is a concept in statistics, which refers to the average of the sum of squares of the difference between each data in the sample and the sample mean, and is the most important and commonly used indicator to measure discrete trends.

Through variance calculation, the distribution law of samples (statistics) can be obtained, and the differences between different samples can be compared.

The calculation formula is as follows:

1. Variance formula:

2. Standard deviation formula (1):

3. Standard deviation formula (2):

For example, the results of the 5 tests of two people are as follows: x: 50, 100, 100, 60, 50, and the average value is e(x)=72;y: Songzhong group 73, 70, 75, 72, 70 average e(y) = 72.

The average score is the same, but x is unstable and deviates greatly from the mean. Variance describes the degree to which a random variable deviates from mathematical expectations. A single deviation is the mean of the deviation from the square that eliminates the influence of the sign, i.e., the deviation from the square, and is denoted as e(x): the direct calculation formula separates the scattered and continuous types.

Another calculation is derived: "The variance is equal to the mean of the sum of the squares of the deviation between each data and its arithmetic mean". Among them, the calculation formulas of discrete type and continuous type are respectively. Called the standard deviation or mean square deviation, variance describes the degree of fluctuation.

The concept of variance:

Variance is a measure of how much dispersion a random variable or set of data is measured by probability theory and statistical variance. Variance in probability theory is used to measure the degree of deviation between a random variable and its mathematical expectation (i.e., the mean). The variance in statistics (sample variance) is the average of the squared values of the difference between each sample value and the mean of the total sample values.

In many practical problems, it is important to study the variance, i.e., the degree of deviation.

Variance is a measure of the difference between the source data and the expected value.

<> variance is in probability theory.

and statistical variance, a measure of how discrete a random variable or set of data is. Such as the average of these five numbers.

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

Variances in probability theory are used to measure random variables and their mathematical expectations.

i.e. the degree of deviation between the mean. The variance in statistics (sample variance) is the average of the squared values of the difference between each sample value and the mean of the total sample acre value. In many practical problems, the degree of deviation is of great significance.

Variance is a measure of the difference between the source data and the expected value.

For two-dimensional random variables (x,y).

variance var(2x-y).

var(2x) + var(y)-2cov(2x,y)4var(x)+var(y)-4cov(x,y) Because x,y is independent, i.e., x,y is not correlated, the covariance cov(x,y) = 04var(x)+var(y).

Example

It is known that the true length of a part is a, and now it is measured 10 times with two instruments A and B, and the measurement pants elimination result x is represented by a point on the coordinates, as shown in Figure 1: the measurement result of instrument A: a, and the measurement result of instrument B: all are a.

The mean of the measurements from both instruments is A. However, if we evaluate the pros and cons of the two instruments with the above results, it is clear that we will assume that the performance of instrument B is better, because the measurement results of the instrument B are concentrated around the mean.

It can be seen that it is necessary to study the degree of deviation of the random variable from its mean. So, what measure is used to measure the degree of deviation? It is easy to see e[|x-e[x]|] measures the degree to which a random variable deviates from its mean e(x).

However, due to the fact that the above equation has an absolute value, it is inconvenient to calculate, and the numerical characteristic of the quantity e[(x-e[x])2] is usually the variance.

Data stability is calculated as follows:

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

where x is the mean of the samples, n is the number of samples, xi is the individuals, and s 2 is the variance.

Statistical significance.

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 relatively concentrated, the sum of squares of the difference between the individual 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 differences between the data in the sample and the sample mean is called the sample variance; The arithmetic square root of the sample variance is called the sample standard deviation. Both sample variance and sample standard deviation are measures of the fluctuation of a sample, and the larger the sample variance or sample standard deviation, the greater the fluctuation of the sample data.

Variance: s 2 = [(x1-x) 2+(x2-x) 2+(x3-x) 2+....+xn-x)^2]/n

x1, x2 ,..xn is the sample data, and x is x1, x2 ,..The mean of xn, where n is the number of samples late, and s is the standard deviation.

Use the square formula for parentheses to get :

s^2=[(x1^2-2x1x+x^2)+(x2^2-2x2x+x^2)+.xn^2-2xnx+x^2)]/n

x1^2+x2^2+..xn^2)-(2x1x+2x2x+..2xnx)+(x^2+x^2+..x^2)]/n

x1^2+x2^2+..xn^2)-2x*(x1+x2+..xn)+nx 2] n, [Note due to x1+x2+..xn=n*x】

x1^2+x2^2+..xn 2)-2x*nx+nx 2] yard forward n

x1^2+x2^2+.)nx^2]/n

Variance is a commonly used indicator in statistics to describe the degree of data dispersion. In data analysis, we often need to calculate variance to assess the volatility of the data. Below we will go into detail about how variance is calculated.

2 = xi - 2 / n

In statistics, variance is calculated in a variety of ways, the most commonly used of which is the calculation of variance for simple random samples. The formula for calculating the variance of a simple random sample is as follows:

The calculation steps of the above formula are as follows:

The calculation steps of the above formula are as follows:

where 2 is the population variance, xi is the ith sample value, which is the mean of the population, and n is the population capacity.

The calculation steps of the above formula are as follows:

The calculation steps of the above formula are as follows:

2.Subtract the population mean from each sample value xi to get the difference between each sample value and the population mean.

2.Subtract the mean x from each sample value xi to get the difference between each sample value and the mean.

Population variance is calculated in a similar way to sample variance, but the mean of the population is used when calculating the population variance, not the mean x of the sample.

In conclusion, variance is one of the important indicators to evaluate the degree of data dispersion, and by understanding the calculation method of variance, the data can be better understood and analyzed.

^2 = xi - 2 / n

s2 = xi - x ) 2 n - 1) The above formula is calculated as follows:

1.Calculate the average of the population.

1.Calculate the mean value of the sample x.

4.Divide the total sum of squares by the population capacity n to get the population variance of 2.