2. Arithmetic average.

Arithmetic average refers to the sum of all data in a set of data divided by the number of data, which is an indicator reflecting the trend in data concentration. The formula is: average value = (a1+a2+…+an)/n.

3. Weighted average.

If n numbers x 1, x2, ... ……xn are w 1, w2, ... wn, then the weighted average of these n numbers is (x1w/+x2w2+...+xnwn)/(w/kloc). ...

An obvious advantage of the average value is that it can make use of the characteristics of all data and is relatively easy to calculate. In addition, in mathematics, the average value is a statistic that minimizes the sum of squares of errors, that is to say, using the average value to represent data can minimize the secondary loss.

Therefore, the average value is a commonly used statistic in mathematics. However, the average also has some disadvantages, precisely because it uses all the information of data, and the average is easily influenced by extreme data.

Special Description of Arithmetic Average

1, the weighted arithmetic mean is affected by two factors at the same time, one is the size of each group, and the other is the distribution frequency of each group. Under the condition of constant value, the more frequency a group appears, the greater the effect of the group's value on the average value, and vice versa.

Frequency plays an important role in weighted arithmetic average, which is also the significance of weighted arithmetic average.

2. Arithmetic average is easily influenced by extreme value. For example, there are the following data: 5, 7, 5, 4, 6, 7, 8, 5, 4, 7, 8, 6, 20. The average value of all data is 7. 1. In fact, most data (including 10) are less than 7. If 20 is removed, the remaining 10. It can be seen that the appearance of extreme value will interfere with the authenticity of the average value.