According to the different formats of sample data, this paper introduces two common calculation methods of arithmetic mean, one is simple arithmetic mean, and the other is weighted arithmetic mean.
There are usually two data formats in data analysis. One is the regular format (unweighted format), and the other is the weighted data format. The explanation is as follows:
Conventional data format → Simple arithmetic mean
In the first conventional format (unweighted format), one line represents one sample, and if there are 100 samples, it is 100 line; A column represents an attribute; This format is the most common, and this data format can do any analysis. Because it carries all the most original data information. Similar to the following table:
At this point, the simple arithmetic average calculation is used, and the formula is:
This is the method we learned in primary school to calculate the average value. Add up each number of this set of data to be calculated and then divide it by the number of samples.
Weighted data format → weighted arithmetic average
For example, 100 samples were collected, and finally there were 40 males and 60 females. The input data is summary statistics, and a single column (or multiple columns) indicates the number of samples in each category; Table below:
This data format is not original data, but after grouping and sorting, it is calculated by weighted arithmetic average, and the formula is:
Extreme value situation
As can be seen from the formula, the calculation of the average value is related to each value of the sample, so it is more representative. But if there is no extreme value in the data, the extreme value refers to the maximum or minimum value in a set of data. If there are extreme values, the average value may not be suitable to describe the concentration of the overall data.
For example, the test scores of five students in a class are 10 70 80 90 100 respectively.
According to the data format, calculate its arithmetic average:
M(5 students) = (10+70+80+90+100)/5
=70
The average arithmetic score of these five students is 70. Observing the original data, four students scored 70 points or more, and only one student scored below 70 points. Judging from this, it is not appropriate to use 70 points to represent the concentration of this set of data. Look at the original data, it is the extreme value of 10, which lowers the whole average score at once, so we remove the test score of 10 and calculate the arithmetic average of the remaining four students:
M (four students) = (70+80+90+ 100)/4
=85
Eighty-five points can better represent the concentration trend of four students. Two students scored below 85 and two students scored above 85.
You can use SPSSAU for quick analysis:
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