First, what is "original score"? What is "standard score"? The original score is the score obtained directly from the test paper after the exam. The standard score refers to a position quantity obtained through the transformation of the original score, which reflects the position of the examinee's score among all the examinee's scores. So no matter whether the test questions are difficult or easy, no matter whether the overall original score is high or low, the overall standard score has not changed.

Second, how is the standard score calculated? According to the principle of educational statistics, the standard score z is the deviation between the original score and the average score in the standard deviation, which is expressed by a formula (upper right corner).

It is the average score of all candidates in this exam; X is the original score of the examinee's personal income in this exam; S is the standard deviation of the test score.

The standard score has the following properties: (1) the average value is 0 and the standard deviation is1;

(2) Fractions are equidistant and can be added or subtracted;

(3) The conversion from the original score to standard score is linear, which will not change the distribution shape of the original score, nor will it change the position order of the original score. Under normal circumstances, the converted standard score z is a decimal, and there will be a negative value, which is inconvenient in practical use, so it is necessary to carry out linear transformation (T transformation) on the score z:

This is what we usually call standard score. The average value of this standard score is 500, that is to say, if a candidate's standard score is 500, then the student's score is in the middle of the exam. Of course, this is done on the premise of the normal distribution of the original score. If the distribution of the original score does not meet the requirements of normal distribution, it should be normalized first and then converted into standard score. The converted score is called normalized standard score, which is what we call standard score.

3. What are the advantages of using the standard score over the original score?

According to the principle of educational statistics, the significance of converting original scores into standard score can be reflected by the following comparison:

(1) A single standard score can reflect the position of candidates' scores in all candidates' scores, but a single original score cannot. For example, a candidate's original score in a certain subject is 85, so it is impossible to explain his score in this subject, because it is related to the difficulty of the test questions and the overall score of the candidates. If the standard of a certain subject of a candidate is 650, that is, the z score is 1.5, and the percentage corresponding to the normal distribution table is 0.933 19, then we know that the candidate's score exceeds 93.3 19%, which is the standardization of score interpretation.

⑵ The original scores of different disciplines are not comparable, but standard score of different disciplines is comparable. Different subjects have different scores due to the different difficulty of the test questions. For example, a candidate's original Chinese score is 80 and his original math score is 70. Judging from the original score, his Chinese score is better than his math score. However, if the average original score of all candidates in this exam is 86 and the average original score of mathematics is 60, then the candidate's Chinese score is lower than the average level of all candidates, while his math score is higher than the average level of all candidates, that is, the student's math score is substantially better than his Chinese score. Judging from the standard score, its language standard score is less than 500, while its mathematics standard score is above 500. Because the standard score represents the position of the original score in the whole original score, it is comparable.

(3) The original scores of different disciplines cannot be added, but the standard scores of different disciplines are added. Because the original scores of different disciplines are not comparable, they cannot be added up. The results of multi-disciplines can only be added when the average and standard deviation of each discipline are the same, otherwise it is unscientific. The average and standard deviation of the original scores of each subject are generally different, while the average and standard deviation of the standard scores of each subject are basically the same. Therefore, the standard scores of all subjects can be added up.

4. Is the standard total score the weighted average of the standard scores of all subjects?

The standard total score is not the weighted average of the standard scores of all subjects. It is to add the standard scores of all subjects according to the weight to get a weighted sum (referred to as weighted value), and then convert this weighted value into the standard score, and the value obtained is the standard total score.

Five, the city's 2008 senior high school entrance examination results are presented at the same time with the single subject level and the standard total score.

The senior high school entrance examination also began to implement standard score. Over the years, good results have been achieved. In 2007, influenced by the college entrance examination, I tried the original score, and the result proved that the effect was not ideal. There are hundreds of candidates with the same score (for example, there are as many as 300 candidates with a total score of 435 in the senior high school entrance examination in 2007), which is not conducive to high school admission. Our city has decided to still use the standard score in this year's senior high school entrance examination, and the results of the unified examination of subjects are presented at the same time as the single subject level and the standard total score. The scores of single subjects are divided according to the standards of single subjects, and the setting grades and the proportion of each grade are as follows:

A+(5%)、A(20%)、B+(25%)、B(25%)、C+(20%)、C(5%)

The general standard consists of six subjects: Chinese, Mathematics, English, Science, History and Society, and Physical Education. The weights of Chinese, mathematics, English and science are all 1, and the weights of history and society are 0.6. Sports scores are included in the standard total score of senior high school entrance examination with the weight of 8% (the weight of sports scores in 2008 was 5%).