What is the concept of variance, standard deviation?

Standard deviation (standard

deviation)

The average of the distance (mean difference) of each data from the mean, which is the square root after the sum of the squares of the deviation. Denoted by . Therefore, the standard deviation is also a kind of mean.

The standard deviation is the arithmetic square root of the variance.

Standard deviation is a reflection of how discrete a dataset is. If the mean is the same, the standard deviation may not be the same.

For example, if 6 students from each group A and B take the same language test, the score of group A is , and the score of group B is . The mean for both groups is 70, but the standard deviation of group A is a score and the standard deviation of group B is a score, indicating that the gap between students in group A is much larger than that between students in group B.

Standard deviation is also known as standard deviation, or experimental standard deviation.

There is a detailed description of this function in the stdevp function in excel, and the word "standard deviation" is used in the excel Chinese version. However, China's Chinese textbooks usually use "standard deviation".

The formula is shown in Fig. In Excel, the stdevp function is another standard deviation mentioned in the following comment, which is the population standard deviation. In some places in Chinese Traditional Chinese, it may be called "parent standard deviation".

Because there are two definitions, which are used in different contexts:

In the case of a population, the standard deviation formula is divided by n in the root number, and in the case of a sample, the standard deviation formula is divided by (n-1) in the root number, because we are exposed to a large number of samples, so it is common to divide by (n-1) in the root number

Variance and standard deviation are used to describe the volatility (centralized or dispersed) of a set of data, and the square of the standard deviation is the variance.

1. 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 sum of the squares of the difference between each data and its mean.

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.

Second, the standard deviation, in the Chinese environment, is often called mean square deviation, but different from the mean square error, the mean square error is the average of the distance square of each data from the true value, that is, the average of the sum of the squares of the error, the calculation formula is formally close to the variance, its opening is called the root mean square error, the root mean square error is formally close to the standard deviation), the standard deviation is the square root after the square sum of the mean deviation, expressed by . The standard deviation is the arithmetic square root of the variance. Standard deviation is a reflection of how discrete a dataset is.

The standard deviation of a set of data with the same mean is not necessarily the same.

Note: Variance and standard deviation are the most important and commonly used indicators to measure discrete trends.

First of all, the standard deviation is squared and then the variance.

Both are the magnitude of the volatility that manifests it.

Variance is also known as variance and mean square. As a statistic, it is often denoted by the symbol S2, and as an overall parameter, it is denoted by the symbol 2. It is the mean of the difference between each data and the mean of the set of data, i.e., the mean of the square.

Variance, also known as the second-order central moment or second-order dynamic difference in mathematical statistics. It is a very important statistical feature number to measure the degree of data dispersion. Standard deviation is the square root of the variance, often expressed by s or sd.

If it is denoted by , it refers to the standard deviation of the population, and this chapter only discusses the description of a set of data, and does not deal with the overall problem, so the sign of variance in this chapter is s2, and the sign of standard deviation is s. The symbols are different, and their meanings are not exactly the same, and I hope that the reader will pay full attention to this. 2. The significance of variance and standard deviation Variance and standard deviation are the best indicators to indicate the degree of dispersion of a set of data.

The larger the value, the greater the degree of dispersion, and the value ** indicates that the data is relatively concentrated, and it is the most commonly used difference in statistical description and statistical analysis. It basically has the conditions that a good difference should have: it is sensitive, and the variance or standard deviation changes with the change of the value of each data; There are certain calculation formulas that are strictly determined; Easy to calculate; suitable for algebraic operations; It is less affected by sampling changes, that is, the standard deviation or variance of different samples is relatively stable; Plain and simple, this point is a little less than the other differences in the quantity, but its significance is still relatively clear.

In addition to the above, variance also has the characteristics of additiveness, which is the measurement of the sum of various variations in a set of data, which can be used to decompose and determine the variability belonging to different ** (such as between groups, within groups, etc.) and can further explain the impact of each variation on the total results, which is the number of statistical features commonly used in the statistical inference part in the future. In the descriptive statistics, only standard deviation is sufficient to indicate the trend of a set of data. The standard deviation is mathematically superior to all other differences in size, especially when the mean and standard deviation of a set of data are known, and a certain percentage of the data falls within two standard deviations above and below the mean, or three standard deviations.

For any one data set, at least 1 to 1 h2 of data fall within h (real numbers greater than 1) of the mean. (Chebyshev's theorem). For example, if the mean of a certain set of data is 50 and the standard deviation is 5, then at least 75 (1-1 22) data fall between 50-2*5 and 50+2*5, that is, between 40 and 60, and at least 88 9 (1-1 32) data fall between 50-3*5 and 50+3*5 35-65 (h=2,1-1 h2=1-1 22=3 4=75%,h=3, -1 h2=1-1 32=8 9=).

If the data is normally distributed, the data will fall within two standard deviations (95) or three standard deviations (99.) above and below the mean by a larger percentageI read the following address slowly.

1. Standard deviation reflects the degree of dispersion among individuals within the group. It has two characteristics:

The result measured to the degree of distribution is a non-negative value and has the same units as the measured data.

There is a difference between the standard deviation of a total or a random variable and the standard deviation of the number of samples in a subset. In simple terms, standard deviation is a measure of how dispersed the mean of a set of data is. A large standard deviation represents a large difference between the majority of the values and their mean; A small standard deviation means that these values are closer to the mean.

Standard deviation can be used as a measure of uncertainty.

For example, in the physical sciences, when making repeatable measurements, the standard deviation of the set of measured values represents the accuracy of those measurements. When it comes to deciding whether a measured value meets the ** value, the standard deviation of the measured value plays a decisive role

If the measured mean is too far away from the ** value (and is compared to the standard deviation value), the measured value is considered to contradict the ** value. This is easy to understand, because if the measurements fall outside a certain range, it is reasonable to infer that the ** value is correct.

2. Variance: It reflects the degree of deviation between a random variable and its mathematical expectation (i.e., the mean). It has the following characteristics.

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

This property can be generalized to the sum of a finite number of unrelated random variables.

The differences between variance, standard deviation, and covariance are as follows:

1. The concept is different.

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;

The standard deviation is the square root of the arithmetic mean of the square of the deviation of the standard values of each unit of the population from its mean;

Covariance represents the overall error of two variables, unlike variance, which represents the error of only one variable.

2. The calculation method is different.

The variance is calculated as:

where s represents the variance, x1, x2, x3 、..xn represents the individual data in the sample, and m represents the sample average;

Standard deviation = arithmetic square root of variance = s = sqrt(((x1-x) 2 +(x2-x) 2 +xn-x)^2)/n)；

The covariance is calculated as cov(x,y)=e[xy]-e[x]e[y], where e[x] and e[y] are the expected values of the two real random variables x and y.

3. The meaning is different.

Both variance and standard deviation are statistically based on a set of (one-dimensional) data, reflecting the degree of dispersion of a one-dimensional array;

The covariance is a statistic of the two sets of data, reflecting the correlation between the two sets of data.

1. The difference is:

1) Variance is the square mean of the difference between the actual value and the expected value.

2) The standard deviation is the arithmetic square root of the variance.

3) Covariance is rarely used, mainly to measure the correlation between two variables (there are applications in **).

2. Definition of variance: (variance) is a measure of the degree of dispersion of random variables or a set of data when 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).

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.

3. Definition of standard deviation: standard deviation, also commonly known as mean square deviation in Chinese, standard deviation is the square root of the arithmetic mean from the square of the mean deviation, expressed by . The standard deviation is the arithmetic square root of the variance.

Standard deviation is a reflection of how discrete a dataset is. The standard deviation of data for two groups with the same mean may not be the same.

4. Definition of covariance: Covariance analysis is a statistical analysis method based on ANOVA and regression analysis. ANOVA is the difference in the influence of different levels of factors on experimental indicators from the perspective of quality factors.

Generally speaking, the quality factor can be artificially controlled. Regression analysis is based on the quantitative factor, and the quantitative relationship between the experimental index and one (or several) factors is studied by establishing the regression equation. But in most cases, the quantity factor cannot be artificially controlled.

62616964757a686964616fe58685e5aeb9313334313733333, covariance understanding and difference"> understanding and differentiation of variance, standard deviation, and covariance.

1. Variance. It is a measure of the degree of deviation between a random variable and its mathematical expectation (i.e., the mean).

Calculation: The average of the squares of the difference between the individual data and the mean.

2. Standard deviation.

It can reflect the degree of dispersion of a data set.

Calculation: Variance open root number.

3. Covariance.

Used to measure the overall error of the two variables. Whereas, variance is a special case of covariance, i.e., when two variables are the same.

Change analysis: 1) If the trend of change of the two variables is consistent, that is, if one of them is greater than its expected value, and the other is also greater than its expected value, then the covariance between the two variables is positive.

2) If the two variables change in opposite directions, i.e., one of them is greater than its expected value and the other is less than its expected value, then the covariance between the two variables is negative.

Calculation: If there are two variables x and y, multiply the "difference between the x value and its mean" by the "difference between the y value and its mean" at each moment to get a product, and then sum the product of each moment and find the mean, which is the covariance.

The variance is the average of the sum of the squares of the deviations of individual data from their arithmetic mean.

The standard deviation is the average of the distance of each data from the mean, and it is the square root after the sum of the squares of the mean deviation.

Covariance is used to measure the overall error of two variables.

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.

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 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 . It is most commonly used in probability statistics as a measure of the degree of statistical distribution. The standard deviation is the arithmetic square root of the variance.

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