The distribution of Z-score has two characteristics: first, the average value of Z-score is equal to 0; Second, its standard deviation is equal to 1. When a group of data is in normal distribution or near normal distribution, the standard of the point equivalent to the average value is 0, the standard of each point above the average value is positive, and the standard of each point below the average value is negative.

Standard score is a numerical value that is unaffected by the original unit of measurement. Its function is not only to show the position of the original data in its distribution, but also to compare the data of different units that cannot be directly compared in the future. For example, compare the position of each student's grades in class grades or compare the grades of a student in two or more exams.

Standard score plays an important role in the statistical analysis of standardized tests. In order to make each test score comparable and additive, and accurately reflect the position of each candidate's score in the overall test, there must be the same unit and reference point. Scores with the same value and meaning are called standard score or Z scores in educational statistics.

For example, the following table shows the college entrance examination results of two candidates. According to the original score, candidate B scored 400, while candidate A scored only 382. If you are admitted according to the total score, you will be admitted to student B. If you are admitted according to the standard score, you will be admitted to student A, because all the scores of candidate A are not lower than the average score, while candidate B's math and foreign languages are lower than the average score. It can be seen that standardized scoring (converted into standard score) has certain advantages.