How do you use the sample standard deviation to get the population standard deviation? 10

The variance is the actual value vs. the expected value.

The average of the squares of the difference. 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 deviation of the batch of data from the average.

and call it the variance of this set of data. Write as s2. In the case of the same sample size, the larger the variance, the greater the fluctuation and the more unstable the data. The standard deviation is the square root of the variance.

Variance and standard deviation are used in different occasions for easy calculation.

Standard deviation in English).

Variance formula. Standard deviation formula.

Here comes the difficulty, the overall standard deviation.

There is a difference between the formula and the standard deviation of the sample, as shown in the figure below.

The standard deviation of the sample formula, the denominator.

It's n-1. Why is the denominator of the standard deviation of the sample n-1 instead of n or n-2?

We use computer modeling, the environment anaconda(

Parameter explanation: Sigma represents the standard deviation of the population.

s denotes the standard deviation of the sample.

ddofvalue=0 means that the standard deviation denominator of the sample is n

ddofvalue=1 means that the sample standard deviation denominator is n-1

ddofvalue=2 indicates that the sample standard deviation denominator is n-2

Algorithm ideas:1Simulate a population (obeying a normal distribution.

of 1000 random numbers.

2.Random sampling (100 random numbers) from the population

3.The standard deviations of the population and the sample are calculated separately and then subtracted to obtain the distance difference.

4.Cycle through 1000 experiments and add up 1000 distances to get the total distance

5.In step 3, n, n-1, and n-2 were taken as the denominator of the standard deviation of the sample, respectively, and finally the dict modes were obtained

Observe the absolute value of dict modes, ddof1. Least.

1. The meaning is different

Sample Criteria. Poor du in the real world, except in certain special cases.

DAO, finding a population version of the true standard deviation is not realistic. Most of the time, the population standard deviation is estimated by taking a certain amount of sample at random and calculating the sample standard deviation.

2. Different usage.

If it is a population, divide by n in the root number of the standard deviation formula, and divide (n 1) in the root number of the standard deviation formula if it is a sample.

The difference is that the denominator of the standard deviation of the sample is n-1

The population standard difference denominator is n

Standard deviation of the sample.

du= [1 (n-1) (xi-x) ]i from 1 to n population standard deviation = zhi f(x) is the population DAO probability density and e(x) is the expectation of the population.

The standard deviation of the sample version is weighted by using the data, and can be calculated as long as there is measurement data, while the standard deviation of the population can be calculated by probability density, which is generally not possible, because in mathematical statistics, the distribution of the population is generally unknown.

The standard deviation of the sample is an approximation of the standard deviation of the population.

As the name suggests, the standard deviation of the population is derived from the whole data and reflects the data characteristics of the population, while the standard deviation of the sample is only derived from part of the data in the population and can only reflect the data characteristics of the selected sample.

The population standard deviation is calculated by dividing by n (n is the number of populations) and the sample standard deviation is divided by (n-1) (n is the sample size). There are subtle differences, but when n is large, the difference is not significant.

Why is the standard denominator of the sample n-1 and the population n?

The standard deviation of a sample is equal to the standard deviation of the population divided by the number of samples under the root sign. Sample standard deviation = [1 (n-1) (xi-x pull) ]i from 1 to n. Population standard deviation = f(x) is the probability density of the population.

e(x) is the overall expectation. If it is a population, the standard deviation formula.

Divide by n in the root number, and in the case of samples, divide by (n-1) in the root of the standard deviation formula, and the difference between the two formulas is one degree of freedom.

n vs. n-1.

Sample:

A specimen is a subset of individuals observed or investigated, and the population is the entirety of the object of study. The general name of the elements to be examined in the population, and the number of individuals in the sample is called the sample capacity.

In general, the content of the sample is with units, for example, in the survey of the visual acuity of 300 middle school students in a middle school, the sample is the visual acuity of 300 middle school students, and the sample size is 300. The process of selecting a sample is called sampling, depending on the object, in the sampling method.

There are also differences.

The standard deviation of the sample is formulated as s= [1 (n-1) (xi-x)] The sample is a subset of the observed or surveyed individuals, and the population is the whole of the study object. The standard deviation is the degree of dispersion of the sample data. The standard deviation is the open square of the mean variance of the sample, which is usually determined relative to the mean of the sample data.

Standard deviation is most commonly used in probability statistics as a measure of the degree of statistical distribution. Standard deviation is defined as 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. It reflects the degree of dispersion between individuals within the group.

In principle, the results measured to the degree of distribution have two properties: they are non-negative values and have the same units as the measured data.

Sampling errorThe size of the use of the meanStandard deviationDescription, i.e., the standard deviation of the sample mean, referred to as standard error.

A sample is drawn from the population, and this sample has a mean. There is more than one sample with the same capacity, and the mean of each sample drawn may also be different, that is, the mean value of the sample also constitutes a statistic.

If the distribution of the population is constant, then the mean of the sampled sample also obeys a fixed distribution. Therefore, the expectation of the sample mean is equal to the expectation of the population, and the standard deviation can be calculated based on whether the population is finite and its population distribution.

Sampling distribution of the sample mean.

The sampling distribution of the sample mean is the distribution formed by the macro mean of all samples, i.e., the probability distribution of .

The sampling distribution of the sample mean is symmetrical in shape. As the sample size n increases, it does not matter whether the original population obeys a normal distribution or not.

The sampling distribution of the sample mean will all tend to be normally distributed, and the mathematical expectation of its distribution.

is the population mean and the variance is 1 n of the population variance. This is the central limit theorem.

central limit theorem）。

Let the population have n elements, and randomly select a sample with a capacity of n, and when the sampling is reset, there are n·n kinds of sampling, which can form n·n different samples, and when the sampling is not repeated, there are n·n possible samples.

A mean can be calculated for each sample, and the distribution formed by these possible sampling means is the distribution of the sample mean. However, in reality, it is not possible to extract all samples, so the probability distribution of the sample mean is actually a theoretical distribution.

Sample standard deviation: (x1-xba) squared + (x2-xba) squared +.xn-xba) and divide by (n-1), then open the root number.

When the nature of the parent population is not clear, we need to use a certain quantity as an estimate, and we need to help understand the nature of the parent number. For example, the sample mean is an estimate of the parent population mean.

When we use only a specific value, i.e., a point on the number line, as an estimate to estimate the nominator, it is called a point estimate.

The purpose of point estimation is based on sample x=(x1, x2...).xi) Estimate the unknown parameters contained in the population distribution or the function g( ) general or g( ) is a certain eigenvalue of the population, such as mathematical expectation, variance, correlation coefficient, etc.

The common methods of point estimation include moment estimation method, ordinal statistics method, maximum likelihood method, least squares method, etc.

Population standard deviation and sample standard deviation are two concepts used in statistics to measure the degree of dispersion of data distribution, and there are the following differences between them:

1.Define Object: Population Standard Deviation is a measure of the dispersion of the population data set to measure the degree of dispersion of the population data. Sample standard deviation is a measure based on a sample data set and is used to estimate the standard deviation of the population.

2.Calculation Method: The standard deviation of the population is calculated as the standard deviation of the population = the variance of the population), where the population variance is the average of the squares of the difference between all data and the population mean.

The sample standard deviation is calculated as sample standard deviation = sample variance), where sample variance is the average of all data squared from the sample mean.

3.Degrees of Freedom: The data of the entire population is taken into account in the calculation of the standard deviation of the population, so there is no concept of degrees of freedom.

The sample mean is used in the calculation of the standard deviation of the sample, so the degrees of freedom within the sample need to be taken into account, which is usually expressed by n-1 (n is the number of samples).

4.Inferred properties: The standard deviation of the population is the degree of the parameters of the population and is therefore determined.

Whereas, the sample standard deviation is an estimate of the population parameter and is therefore a random variable with some uncertainty. The standard deviation of the sample will vary depending on the sample selection.

5.Applications: Population standard deviation is often used to describe the properties and parameters of a population. Sample standard deviation is often used to estimate the standard deviation of a population based on limited sample data, and to perform statistical analyses such as inference and hypothesis testing.

There are some differences between the population standard deviation and the sample standard deviation in terms of calculation method, object, degree of freedom, inference property and application range, etc., and the appropriate standard deviation concept is selected for analysis according to the specific application requirements and data situation.

1. The observation object is different

The standard deviation of the sample is observed or surveyed by a subset of individuals, and the population standard deviation is the entire cluster of the study subject. The number of units of observation contained in the population is usually large or even infinite.

2. The role is different.

The standard deviation of the sample reflects the degree of difference between individuals within the study population, and the standard deviation of the sample indicates the degree of dispersion of the sample data.

Apply. 1. Scratches on the surface of the strip steel plate.

The galvanizing unit of Jiuxiaofu Steel is designed to produce 750,000 tons per year, the unit has strong production continuity and high requirements for surface quality, and its products are mainly used to produce home appliance plates and aluminum-zinc sheets, which have been exported to domestic and foreign markets. Since it was put into production in 2010, it has gone through a long process in solving strip scratch defects.

2. Uncertainty evaluation of the error of the precision pressure indication value.

The precision pressure gauge has the characteristics of simple structure and high cost performance, and has been widely used in industrial and agricultural production and scientific research tests for a long time, and has even been used as a standard seepage and elevation standard equipment for verifying general pressure gauges.