Grade 9 To 12 Students' Understanding Of Standard Daviation

It is the necessary ability for every citizen that they should know the basic statistics knowledge. Following to the contents and teaching hours increasing in the new curriculum for statistics and probability, it is self-evident for the status and importance to this topic. Standard deviation is one of the important indexes to judge the variance in statistics, researching the students' understanding of the concept of stand deviation can be used for reference to the teaching of statistics.This study investigated the grade 9-12 students' comprehension of the concept of standard deviation. Following are the two research questions:â‘ How do they understand the standard deviation for the students of grade 9-12 who have learned it, including both the concept and the formula.â‘¡Without calculating the detail data, how do the students judge the big or small for the standard deviation. We expect to find some strategies when the students use to compare the standard deviations.In the whole research process, this author carried on the investigation to 509 students in grade 9 -12 in the form of test paper and questionnaire. 15 students were interviewed as well. With the data analysis as well as the interview content analysis, this author finally drew the following conclusions:1. The students get a basic knowledge for the standard deviation concept; some of them can use the extreme value to compare the standard deviations. But they are easy to mix the two index function, the standard deviation is referring to the data dispersed level and the average is referring to the data average level.2. The students estimate ability is relatively worse. They know the data variation, but they couldn't do good estimate to the size of the data variation.3. To use the standard deviation formula, the students just can do it in detail digit. They are weakly to the alphabet handling and certificating.4. 9-12 different grades have the significant difference to the comprehension of standard deviation concept. Senior 1 is the best grade which comprehends the concept of standard deviation in three grades, with a basically higher correct rate than the other two grades. Senior 2 and Senior 3 also have certain difference. Senior 2 did a better job than Senior 3. The job junior 3 did is almost the same as that done by Senior 3. 5. The good level students in mathematics have obvious difference in comprehending the concept of standard deviation than normal level and worse level students. But we found no significant difference existing in the normal and worse level students' comprehension of the standard deviation concept6. In the compare of understanding the concept of standard deviation, girls are better than boys. But boys are better than girls in the flexible using of standard deviation formula.Finally, from the result of this study, the author put forward some proposals to the statistical lesson instruction.1) In the teaching of Statistics and Probability, the process should be stressed, practice experience will be important.2) Experiment is important. Students can learn the variation from the experiment data and understand more to the proper variation.3) In the teaching of Statistics, it should be pay more attention to the diagram understanding.