Standard deviation: it is the square root of the arithmetic mean value deviating from the mean square, and is expressed by σ. The standard deviation is the arithmetic square root of variance.
Variance: Variance is a measure of the degree of dispersion when probability theory and statistical variance measure random variables or a group of data. Variance in probability theory is used to measure the deviation between random variables and their mathematical expectations (that is, the mean value). The variance (sample variance) in statistics is the average value of the square of the difference between each sample value and the average value of all sample values.
Range: Range, also known as range error or range, is expressed by R, which is used to represent the difference between the maximum value and the minimum value of the measure of variance in statistical data, that is, the data obtained by subtracting the minimum value from the maximum value. Refers to the difference between the maximum value and the minimum value in a set of data.
Difference:
1, the average difference indicates the concentration trend, and the standard deviation indicates the deviation trend of a group of data. The average difference reflects the average difference between each flag value and the arithmetic average, and is the average of the absolute value of the difference between each data and the average; The standard deviation is the square root of the average sum of deviations from the mean square, which can better reflect the dispersion degree of a data set.
2. Variance is the sum of each number minus the square of the average, and standard deviation is the variance divided by the number of things we care about. Variance = (1/n) [(x1-x _) 2+(x2-x _) 2+...+(xn-x _) 2].
3. The average difference is the arithmetic mean of the absolute value of the deviation between all units in the population and their arithmetic mean. Variance is the average value of the sum of squares of the deviation of each data from its arithmetic mean.
Connection: the larger the range, the less representative the average difference, and vice versa; The greater the standard deviation, the smaller the representativeness of the average difference. On the contrary, the arithmetic square root of variance = standard deviation.
Extended data:
Statistical significance of variance
When the data distribution is scattered (that is, the data fluctuates greatly around the average value), the sum of squares of differences between each data and the average value is large, and the variance is large; When the data distribution is concentrated, the sum of squares of the differences between each data and the average value is very small. Therefore, the greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation.
The average value of the sum of squares of the difference between the data in the sample and the average value of the sample is called sample variance; The arithmetic square root of sample variance is called sample standard deviation. Sample variance and sample standard deviation are both measures of sample fluctuation. The greater the sample variance or standard deviation, the greater the fluctuation of sample data.
Variance and standard deviation are the most important and commonly used indicators to measure discrete trends. Variance is the square of variance of each variable value and the average of its mean, which is the most important method to measure the dispersion degree of numerical data. The standard deviation is the arithmetic square root of variance, expressed by S, and the corresponding variance calculation formula is:
The difference between standard deviation and variance is that the calculation unit of standard deviation and variable is the same, which is clearer than variance, so we often use standard deviation more in analysis.
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