ZH cheese: standard deviation

Standard deviation

Standard deviation (STD dev,standard Deviation)-statistical nouns. A criterion for measuring the degree of dispersion of a data distribution to measure the degree to which the data value deviates from the arithmetic average. The smaller the standard deviation, the less the values deviate from the average, and vice versa. The size of the standard deviation can be measured by the ratio of the standard deviation to the average.

Standard deviation is also referred to as standard deviations, or experimental standards deviation, and standard deviation (Deviation) describes the average distance (from mean difference) of each data deviation from the average, which is the square root of the deviation squared and the average, expressed in σ. The standard deviation is the square root of the variance of the arithmetic. The standard deviation reflects the degree of dispersion of a data set, the smaller the standard deviations, the less the values deviate from the average, and vice versa. The size of the standard deviation can be measured by the ratio of the standard deviation to the average. Two datasets with the same average, the standard deviation may not be the same. For example, 6 students from both groups A and B participated in the same language test, with a score of 95, 85, 75, 65, 55, and 45,b groups with a score of 73, 72, 71, 69, 68, 67. The average of both groups was 70, but the standard deviation for group A should be 18.708, and the standard deviation for Group B should be 2.37, indicating that the gap between students in Group A was much greater than that of Group B students.General standard deviation and sample standard deviationoverall standard deviation:Deviations for the overall data, so on average,Sample Standard deviation:In order to calculate the overall deviation from the overall sampling, using the sample to make the calculated value closer to the overall level, the calculated standard deviation must be scaled moderately, i.e., the sample standard deviation, representing the sample x1,x2,..., xn mean value. The overall standard deviation, which represents the mean value of the overall x. Example: There is a set of numbers 200, 50, 100, 200, to find their sample standard deviation. = (200+50+100+200)/4 = 550/4 = 137.5 = [(200-137.5) ^2+ (50-137.5) ^2+ (100-137.5) ^2+ (200-137.5) ^2]/(4-1) sample standard deviation S = Sqrt (s^2 ) =75 Note: Grade eight (below) Shanghai Science and Technology publishing 21.2 the standard deviation in the dispersion degree of the data is the overall standard deviationCalculation StepsSample Standard deviationThe calculation steps are: Step one, (each sample data minus the average of all the data in the sample). Step two, the sum of the squares of each value obtained by step one. Step three, divide the result of step Two (n-1) ("n" refers to the number of samples). Step four, the square root of the value obtained from step three is the standard deviation of sampling.Overall standard deviationThe calculation steps are: Step one, (each sample data minus the average of overall data). Step two, the sum of the squares of each value obtained by step one. Step three, divide the result of step two by N ("n" refers to the total number). Step four, the square root of the value from step three is the general standard deviation.

ZH cheese: standard deviation