arithmetic average
Arithmetic average (Average) is the result of dividing a group of data by the number of data. It is a commonly used statistic to measure the level of data and is often used in parameter estimation and hypothesis testing. For example, the average wage of employees is used to measure the general level of employees’ wages, and the average weight is used to observe whether a certain group of people is overweight or not. Average is widely used, but the calculation method is simple, which is equal to the sum of all the observed values of a variable and then divided by the number of observed values.
According to the different data, there are different formulas for calculating the arithmetic mean. The average calculated from ungrouped data is called simple average. Suppose a set of sample data is
, the sample size isN, then the simple sample average is used
Said, the calculation formula is:
If there are many original data and they are grouped into frequency distribution series, then the weighted arithmetic average should be used to calculate the arithmetic average, that is, the values of each group of variables should be multiplied by the corresponding frequencies, and then added and summed, and then divided by the total frequency. If the data is divided intoK groups, the calculation formula is:
