The measurement unit and dimension of variance are not easy to explain in the economic sense, so the arithmetic square root-standard deviation of variance is often used to measure the difference of statistical data in practical statistical work.
Standard deviation, also called mean square deviation, is generally expressed by σ. The calculation of variance and standard deviation is also divided into simple average method and weighted average method. In addition, the formula is slightly different for population data and sample data.
Extended data:
I. Relevant history
The word "variance" was first put forward by ronald fisher in his paper "Genetic Relationship Supported by Mendel Genetics".
Second, the 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.
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