If the two population averages are different, should they be used when comparing the degree of dispe

Reason: When it is necessary to compare the dispersion degree of two sets of data, if the measurement scale of the two sets of data is too different, or the dimension of the data.

, using the standard deviation directly.

It is not appropriate to make a comparison, and the coefficient of variation should be eliminated by the influence of the scale and dimension of the measurement.

This can be done by the ratio of the standard deviation of the raw data to the mean of the raw data.

The coefficient of variation has no dimension, so that an objective comparison can be made. In fact, the coefficient of variation, like the range, standard deviation, and variance, can be considered to be absolute values that reflect the degree of dispersion of the data.

The size of the data is not only affected by the degree of dispersion of the variable values, but also by the average size of the variable values.

Extended Materials. Advantages and disadvantages of the coefficient of variation:

1. Advantages: Compared with standard deviation, the advantage of the coefficient of variation is that it does not need to refer to the average of the data.

The coefficient of variation is dimensionless, so when comparing two sets of data with different dimensions or different means, the coefficient of variation should be used as a reference for comparison, rather than standard deviation.

2. Defects: When the average value is close to 0, a small disturbance will also have a huge impact on the coefficient of variation, so the accuracy is insufficient.

The coefficient of variation cannot develop a confidence interval similar to the mean.

tools.

The dispersion coefficient reflects the degree of dispersion on the unit mean, and is often used to compare the degree of dispersion of two population means with unequal values. If the means of the two populations are equal, the coefficient of comparison standard deviation is equivalent to the standard deviation of comparison.

The ratio of the standard deviation of a set of data to its corresponding mean is a relative indicator of the dispersion of the measured data, and its function is mainly used to compare the dispersion of different groups of data. It is calculated as v=s (the average of x).

The standard coefficient of variation is the ratio of the variation index of a set of data to its average index, which is a relative variation index.

Variance is in probability theory.

and statistical variance measure random variables.

or a measure of how discrete a set of data is.

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

Variance is a measure of source data and expected values.

A measure of the difference in difference.

The term "variance" was first coined by Ronald Fisher.

Statistics: 1. When the data distribution is relatively 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.

2. The mean of the sum of 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. Both sample lead variance and sample standard deviation measure the size of a sample's fluctuation, and the larger the sample variance or sample standard deviation, the greater the Buchang fluctuation of the sample data.

3. Variance and standard deviation are the most important and commonly used indicators to measure discrete trends. Variance is the mean of the square of the deviation between the values of each variable and its mean, and it is the most important way to measure the degree of dispersion of numerical data. The standard deviation is the arithmetic square root of the variance, denoted by s.

When comparing the dispersion of two sets of data, it is not possible to compare their standard deviations.

When comparing the degree of dispersion of two sets of data, it is not possible to directly compare their standard deviations because the two sets of data have different units of measurement.

Common ways of data dispersion:

1. Extremely poor. It reflects the numerical range of the data sample, and is the most basic way to measure the degree of data dispersion, which is the simplest of all methods, but it is greatly affected by the extreme value.

2. Quarttile difference.

It reflects the dispersion of the middle 50% of the data, the smaller the value indicates the more concentrated the data, the larger the value indicates the more discrete the data, and because the median is between the quartiles, the interquartile difference also shows the degree of representation of the median to the data sample, the smaller the higher the degree of representation, and the larger the degree of representation, the lower the degree of representation. Limb envy.

3. Average difference.

The larger the mean difference, the greater the dispersion of the data, and the smaller the dispersion of the data.

Dispersion:

The degree of dispersion refers to the degree of difference between the values of the observed variables, which is an indicator used to measure the size of the risk. A central trend describes a representative value at the center of the distribution of a dataset, or at the general level. For the analysis of the overall distribution, the analysis of this dimension alone is obviously not enough.

Mean deviation & standard deviation are absolute indicators of how dispersed the data is. When the mean of two sets of data is not equal, or the unit of measurement is not the same, the dispersion and standard deviation cannot be used to compare the degree of dispersion between the data. It is necessary to use a relative measure of the degree of dispersion, the dispersion coefficient, also called"Standard deviation coefficient", denoted by CV.

Answer]: Oak sells d

The discrete coefficient can eliminate the influence of the absolute number and the unit on the comma value, and more truly reflect the difference in the dispersion degree between different groups of data.

No, it is the variance that indicates how discrete the data is. Variance is a measure of how much dispersion a random variable or set of data is measured by probability theory and statistical variance.

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. Population variance is calculated by the formula:

2 is the population variance, x is the variable, is the population mean, and n is the population number of cases.

Brother should be mistaken, the smaller the coefficient of variation, the smaller the degree of variation (the smaller the fluctuation).

1.In short, the CV value is the standard deviation after removing the dimension, and the standard deviation is divided by the mean value.

2.The cv value is used to measure the results of the parallel experiments of the array, and then the dispersion of the population is inferred, which is the degree of dispersion of the test data, which belongs to descriptive statistics.

3.Generally speaking, according to different populations, the calculation of CV value should not be less than 3 data, preferably more than 10, and the accuracy of inference with CV when the sample size is too large is not enough.

4.For the process route has been running for a period of time and is not in the exploration stage, the CV value can be inferred with reference to the following: when the CV value is less than 1%, it means that the data discrete degree is small; Between 1% and 2%, the data dispersion is normal; 2%-3%, indicating that the data dispersion is acceptable; When it is greater than 4%, it indicates that the data dispersion is large. The larger the data, the more unstable the routing.

5.For the process route in the exploration stage, it is generally considered that if the CV value is used to infer the population, the inference dispersion degree is acceptable if it is less than 10%.

However, it should be noted that since the CV value is only descriptive statistics, in order to obtain more accurate inferences of data volatility, process capacity or significant differences, it is recommended to use tools such as SPC, CPK, hypothesis testing, analysis of variance, and trend analysis. -

No, it should be that the larger the variance, the greater the dispersion of the data.

No, the greater the average difference, the greater the degree of dispersion.

I remember that in the Introduction and Mathematical Statistics class, I talked about three criteria for measuring a statistic: unbiasedness, validity, and consistency.

As long as these three points are met, this statistic can reflect the real situation.

Standard deviation. It is precisely because the square is squared and squared that the dimension is determined.

It is consistent with the original, so that the comparison becomes possible. And it has practical implications, for example, for a random current (a random process, the mean of which is considered to be DC and the standard deviation is considered to be AC. There are many more that have been used in practice. Therefore, they should not be denied.

For the mean difference, it seems to have a clear meaning, but it is also taken in absolute terms.

Ah, there is no reason to intuitively think that absolute values are better than square re-squares. If it can be proven to be unbiased, valid, and consistent, then it is fine, and vice versa.

That's right. Because the larger the standard deviation, the greater the sum of the difference between the average and the mean in that set of data.

For example, there are two sets of data:

a) 1,2,3, the mean is 2, the standard deviation is (1+0+1) 3= 2 3b) 1,2,6, the mean is 3, the standard deviation is (2+1+9) 3=2 2 3<2, that is, the standard deviation of the data in group b is large, which fully reflects the large dispersion of 1, 2, 6.

It's not exact, but it's correct.

That's right. Because the larger the standard deviation, the greater the sum of the difference between the mean and the mean in the hermit data of the group.

For example, there are two sets of data:

a) 1,2,3, the mean is 2, the standard deviation is (1+0+1) 3= 2 3b) 1,2,6, the mean is spike 3, and the standard deviation is (2+1+9) 3=2