After the test, the standard score is called the original score, which is directly evaluated by the candidates according to the scoring standard.

The original score reflects the number of questions correctly answered by candidates, or the degree of correct answers. But the original score can't directly reflect the differences between candidates, can't describe the position of candidates after comparison, and can't explain what scores candidates should get in other equivalence tests.

Derived score is derived from the original score according to certain rules, and its purpose is to further solve the unsolved problems in the original score, or to better and more scientifically explain the meaning of the score, combine the scores and realize the equivalence of the scores. This process of converting original scores into derived scores is called score conversion.

There are many kinds of derivative scores, the most commonly used are percentile and standard score. Standard score is a relative position quantity derived from the original score, which is used to explain the relative position of the original score in this batch of scores.

The solution is as follows: Z=X-X-/S where x is the original score, X- is the average of the original score, and s is the standard deviation of the original score. Z-score takes the average value of a batch of scores as the reference point and expresses the distance in standard deviation.

It consists of a symbol and an absolute value. The symbol indicates whether the original score is greater than or less than the average, and the absolute value indicates how far the original score is from the average. After a batch of scores are all converted into Z scores, the whole distribution pattern has not changed.

Z-score accurately describes the relative position of a score in a batch of scores. However, because Z-score is negative, the number is often small, so it is not easy to be understood and applied. Therefore, people further transformed the Z-score, thus developing a series of other forms of standard score.

The conversion formula is: Z'=αZ+β, where z' is the standard score of other forms, α is the slope of the conversion equation, and β is the intercept of the conversion equation. Standard score, used in the national unified entrance examination for colleges and universities in China, was converted by the method just introduced.

That is, in the formula of T=500+ 100Z, 500 is the average score and 100 is the standard deviation. The establishment of standard score system should generally consist of the following links: ① The provinces still organize scores according to the previous methods, and then synthesize the original scores of candidates in all subjects and count the number of candidates in all subjects and scores. ② The examination center of the State Education Commission, with the cooperation of some provincial examination institutions, carries out the score equivalence between the current year and previous years.

The examination center of the State Education Commission determines the conversion relationship between the original score and standard score, and the provincial examination institutions get the provincial norm scale score according to the conversion relationship. (provinces can make some fine-tuning according to the specific situation of score distribution when converting) ③ Provincial examination institutions announce the scores of provincial norm scale.

(Original scores are not published) The standard sub-system of college entrance examination consists of norm scale score (including national norm and provincial norm) and equivalent scale score. Specifically, the score of the norm scale reflects the position of the candidate's score in an exam, and the score value is related to this position.

Because the college entrance examination is a unified national examination, which is admitted by provinces, there are two situations in standard score conversion: one is to convert the scores of candidates in the whole country, and the other is to convert the scores of candidates in all provinces, so that the scores of the norm scale established in this way can accurately describe the position of candidates' scores in the whole, so that the scores of different disciplines can be compared, but not year by year. In order to make up for this deficiency, it is necessary to increase the score of the equivalence scale.

The understanding and use of standard score to norm conversion score is based on the purpose of college entrance examination and the principle of normal distribution, and the original score is converted into standard score. The average score of this standard score is 500, and the standard deviation is 100. Each norm conversion score has a definite correspondence with the proportion of the number of candidates below this score to the total number of candidates.

If a candidate's physics college entrance examination score is 690, we can check the comparison table of the standard score and percentage score of the college entrance examination and get the proportion of candidates who are lower than the candidate in the total number of candidates. The corresponding proportion of 690 points in the lookup table is 097 127998 (that is, 97 127998%). If the student was a science and engineering candidate in a province last year, and the number of science and engineering candidates last year was 9724, then he exceeded 9445, and about 279 candidates scored higher than him (algorithm: 9724 * (65438)).

In addition, it is emphasized once again that the scores of all subjects and comprehensive scores of candidates are expressed by the scores of norm scale, and the sum of the scores of all subjects is not equal to the comprehensive score. The comprehensive score is synthesized according to the standards of each subject, and then obtained by the score conversion method of the norm scale.

Please don't confuse it with the original total score, and don't mistakenly think that the comprehensive score is the average score of the standard scores of all subjects. In the provinces where the original scores are used, after the candidates know their scores and total scores in all subjects, they should use the admission scores of various schools to measure their scores, and then estimate what kind of schools they can attend.

But in the estimation, because you can't know your position among all the candidates, you are often blind. After using the standard score, candidates can easily know where their total score and scores in all subjects are, and then more accurately estimate and predict what kind of schools they can attend and how big their scale is according to the position of admission scores in the norm score scale.

After the conversion of standard score, after the college entrance examination, the examination institution will send the report card to the candidates and save it in the file: test number, name, language, mathematics, foreign language physics, comprehensive score, 100505 16, Zhang Hua 592 598 642 58 19 636, grade, 82/kloc. The notice of 9 13 results means that Zhang Hua's comprehensive score is 636, and the percentage score is 9 13, so that we can know Zhang Hua's position among science and engineering candidates in the province, that is, 9 1. 3% of the candidates scored lower than Zhang Hua. The meaning of academic performance is the same.

Because all subjects have the same reference point, we can also make comparisons. In this way, we can easily see that Zhang Hua is good at foreign languages and poor at physics.

Another example is that the comprehensive score of a science and engineering candidate is 695, and the corresponding percentage score is 974. In that year, the total number of science and engineering candidates was 1 10285, and there were about 2822 undergraduate students or above, while the admission score for science and engineering undergraduates was that year.

Noun explanation: standard score.

After the test, the standard score is called the original score, which is directly evaluated by the candidates according to the scoring standard.

The original score reflects the number of questions correctly answered by candidates, or the degree of correct answers. But the original score can't directly reflect the differences between candidates, can't describe the position of candidates after comparison, and can't explain what scores candidates should get in other equivalence tests.

Derived score is derived from the original score according to certain rules, and its purpose is to further solve the unsolved problems in the original score, or to better and more scientifically explain the meaning of the score, combine the scores and realize the equivalence of the scores. This process of converting original scores into derived scores is called score conversion.

There are many kinds of derivative scores, the most commonly used are percentile and standard score. Standard score is a relative position quantity derived from the original score, which is used to explain the relative position of the original score in this batch of scores.

The solution is as follows: Z=X-X-/S where x is the original score, X- is the average of the original score, and s is the standard deviation of the original score. Z-score takes the average value of a batch of scores as the reference point and expresses the distance in standard deviation.

It consists of a symbol and an absolute value. The symbol indicates whether the original score is greater than or less than the average, and the absolute value indicates how far the original score is from the average. After a batch of scores are all converted into Z scores, the whole distribution pattern has not changed.

Z-score accurately describes the relative position of a score in a batch of scores. However, because Z-score is negative, the number is often small, so it is not easy to be understood and applied. Therefore, people further transformed the Z-score, thus developing a series of other forms of standard score.

The general conversion formula is: Z'=αZ+β, where z' is the standard score of other forms, α is the slope of the conversion equation, and β is the intercept of the conversion equation. Standard score, used in the national unified entrance examination for colleges and universities in China, was converted by the method just introduced.

That is, in the formula of T=500+ 100Z, 500 is the average score and 100 is the standard deviation. The establishment of standard score system should generally consist of the following links: ① The provinces still organize scores according to the previous methods, and then synthesize the original scores of candidates in all subjects and count the number of candidates in all subjects and scores. ② The examination center of the State Education Commission, with the cooperation of some provincial examination institutions, carries out the score equivalence between the current year and previous years.

The examination center of the State Education Commission determines the conversion relationship between the original score and standard score, and the provincial examination institutions get the provincial norm scale score according to the conversion relationship. (provinces can make some fine-tuning according to the specific situation of score distribution when converting) ③ Provincial examination institutions announce the scores of provincial norm scale.

(Original scores are not published) The standard sub-system of college entrance examination consists of norm scale score (including national norm and provincial norm) and equivalent scale score. Specifically, the score of the norm scale reflects the position of the candidate's score in an exam, and the score value is related to this position.

Because the college entrance examination is a unified national examination, which is admitted by provinces, there are two situations in standard score conversion: one is to convert the scores of candidates in the whole country, and the other is to convert the scores of candidates in all provinces, so that the scores of the norm scale established in this way can accurately describe the position of candidates' scores in the whole, so that the scores of different disciplines can be compared, but not year by year. In order to make up for this deficiency, it is necessary to increase the score of the equivalence scale.

The understanding and use of standard score to norm conversion score is based on the purpose of college entrance examination and the principle of normal distribution, and the original score is converted into standard score. The average score of this standard score is 500, and the standard deviation is 100. Each norm conversion score has a definite correspondence with the proportion of the number of candidates below this score to the total number of candidates.

If a candidate's physics college entrance examination score is 690, we can check the comparison table of the standard score and percentage score of the college entrance examination and get the proportion of candidates who are lower than the candidate in the total number of candidates. The corresponding proportion of 690 points in the lookup table is 097 127998 (that is, 97 127998%). If the student was a science and engineering candidate in a province last year, and the number of science and engineering candidates last year was 9724, then he exceeded 9445, and about 279 candidates scored higher than him (algorithm: 9724 * (65438)).

In addition, it is emphasized once again that the scores of all subjects and comprehensive scores of candidates are expressed by the scores of norm scale, and the sum of the scores of all subjects is not equal to the comprehensive score. The comprehensive score is synthesized according to the standards of each subject, and then obtained by the score conversion method of the norm scale.

Please don't confuse it with the original total score, and don't mistakenly think that the comprehensive score is the average score of the standard scores of all subjects. In the provinces where the original scores are used, after the candidates know their scores and total scores in all subjects, they should use the admission scores of various schools to measure their scores, and then estimate what kind of schools they can attend.

But in the estimation, because you can't know your position among all the candidates, you are often blind. After using the standard score, candidates can easily know where their total score and scores in all subjects are, and then more accurately estimate and predict what kind of schools they can attend and how big their scale is according to the position of admission scores in the norm score scale.

After the conversion of standard score, after the college entrance examination, the examination institution will send the report card to the candidates and save it in the file: test number, name, language, mathematics, foreign language physics, comprehensive score, 100505 16, Zhang Hua 592 598 642 58 19 636, grade, 82/kloc. The 9 13 grade notice means that Zhang Hua's comprehensive grade is 636, and the percentage grade is 9 13, so that we can know Zhang Hua's position among the science and engineering candidates in the province, that is, 9 1. 3% of the candidates scored lower than Zhang Hua. The meaning of academic performance is the same.

Because all subjects have the same reference point, we can also make comparisons. In this way, we can easily see that Zhang Hua is good at foreign languages and poor at physics.

Another example is that the comprehensive score of a science and engineering candidate is 695, and the corresponding percentage score is 974. In that year, the total number of science and engineering candidates was 1 10285, and there were about 2822 undergraduate students or above, while the admission score for science and engineering undergraduates was 633.

Explanation of nouns in z-score diagram

Z-score can answer this question: "How many standard deviations does a given score have from the average?" Scores above the average will get a positive standard score, and scores below the average will get a negative standard score.

Z-score is a way to see the relative position of the score in the distribution. Z score can truly reflect the relative standard distance of the average value of fractional distance.

If we convert each score into a z-score, then each z-score will represent the distance or deviation between a specific score and the average in the standard deviation. The original score in the data with normal distribution is converted into Z score. By consulting the table of Z score area under normal curve, we can know the area between the average value and Z score, and then know the percentage grade of the original score in the data * * *.

The sum of squares of Z score of a series is equal to the number of data in the series, and the standard deviation and variance of Z score are both 1. The average value is 0.