It reflects the trend of data concentration and depicts the average level of a group of data. Simple arithmetic mean is the sum of all the data in a set of data divided by the number of data. For example, directly add up the wheat yield of each plot to get the total output, and then divide it by the total number of acres to get the average yield per mu.
2. Weighted arithmetic average is to multiply variables by weights to get the total score, add the weights to get the total score, and then divide the former by the latter. It is suitable for calculating the average of grouping statistics.
If the output of each plot is divided into several groups according to different production levels, the output of each group is multiplied by the number of plots in each group to get the total output of each group, and then the total output of all plots is added and divided by the total number of plots. The average yield per mu calculated in this way is called weighted arithmetic average.
The advantage of arithmetic average is that it makes use of the characteristics of all data. However, it also has some shortcomings, precisely because it uses all the information of data and is easily influenced by extreme data.
3. Geometric mean
The nth root of the product of n observations is the geometric mean. According to different data conditions, geometric mean can be divided into weighted and unweighted.
4. Harmonic average
Harmonic average is a kind of average. But statistical harmonic mean is different from mathematical harmonic mean. In mathematics, harmonic average and arithmetic average are independent and self-sufficient. The calculation results are different, and the former is always smaller than the latter.
5. Weighted average
The weighted average is the average of different specific gravity data. Weighted average is to calculate the original data in a reasonable proportion. If x 1 appears f 1 time, x2 appears f2 times, …, xk appears fk times in n numbers, then
It is called the weighted average of x 1, x2, …, xk. F 1, f2, …, fk are the weights of x 1, x2, …, xk.
Extended data
Precautions when using the average value:
When using the average index, we should pay attention not only to the total average, but also to the average of the classified indicators, which helps us to use the average correctly and make a comparative analysis.
For example, when using the consumer price index (CPI), we should not only use the total CPI index, but also use the indexes of food, clothing and other major categories, and sometimes use the indexes of specific small commodities such as grain, meat and poultry.
For example, in the context of the rapid rise in food prices, people feel that the prices of certain foods such as vegetables, fruits, grain and oil have risen very high, but the food price index published by the National Bureau of Statistics is not that high.
One of the main reasons is that the food price index is the weighted arithmetic average of various specific food prices, reflecting the average level of food price changes. In the process of buying goods, people tend to remember the approximate price level of a commodity before and after two points, so as to get the increase of the commodity, instead of calculating the price increase of a commodity by weighted average.
If you compare your personal experience with the price increase of vegetables, fruits, grain and oil, you will get more accurate results. For another example, we can see the national average level by using the average annual salary of employees in urban non-private units.
You can also see the average wage data of enterprise employees by region, industry and registered type. Through the use of these classified indicators, we can better reflect the wage level in specific fields.
Baidu Encyclopedia-Average