Range refers to the difference between the maximum value and the minimum value in a group of measured values, also known as range error or full scale, which is expressed by R. It is the maximum range of the change of the mark value and the simplest indicator to measure the change of the mark.
The meaning 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.
The purpose and significance of the limit range:
In statistics, range is often used to describe the degree of dispersion of a set of data, reflecting the range of variation and dispersion of variable distribution. The difference between the standard values of any two units in the group cannot exceed the range. At the same time, it can reflect the amplitude of a group of data fluctuations. The larger the range, the greater the dispersion, and vice versa.
Range only indicates the maximum discrete range of the measured values, and fails to use all the information of the measured values and reflect the consistency between the measured values in detail. Range is a biased estimate of the population standard deviation, which can be used as an unbiased estimate of the population standard deviation when multiplied by the correction coefficient. Its advantages are simple calculation, intuitive meaning and convenient application, so it is still widely used in data statistical processing. However, it only depends on the level of two extreme values, can not reflect the distribution of variables between them, and is easily affected by extreme values.