# Statistics and Computing

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1.0Introduction

This report will cover the distribution of final exam results for BSB123 and what factors influence the results. Factors that will be considered are the gender of the student, whether the student is studying a double or single degree, the results from the weekly quiz’s and the grade achieved on the mid semester report. The presence of outliers will be determined to help analyse the accuracy of the data. There are an infinite number of internal and external factors that contribute to the outcome of a single exam result. Beaty, & Barling (1982) explains how factors such as stress and anxiety can contribute to low test results and they give several self help solutions of how to boost ones success. This report will focuses mainly on quantitative data that can be easily analysed and allows for clear observations to be given about the correlation each evaluated factor has on the final exam result.

2.0 Outliers

The first step in analysing the data is determining if outliers exists within the data. The presence of outliers must be evaluated because their existence could distort the data and make it inaccurate. In order to determine if outliers exist the average and standard deviation must be calculated in order to calculate the Z score, which will show, wither or not outliers exist. In this instance to outliers where found present in the data set as all of the data fell within the +3,-3 range, the largest positive outlier was 2.46 and the largest negative outlier was -1.90. It is important to note the even if any outliers where found they would not necessarily make the analysis more accurate as (Baragona, Battaglia, & Poli, 2011, p. 159-197) explain it all depends about the interpretation of the data.

3.0 Distribution of final exam results

This section shows the varying levels of final exam results from students in BSB123. The figure below shows the different grades from the 705 students. They are represented using a bar chart. Figure 1.0

The distribution shown here is a simple measurement of how the exam results are distributed among the students. The data is an asymmetrical right skewed or positive distribution of 0.46. The greatest amounts of score are seen in the right tail above the mean with a much smaller amount of score being observed in the left tail. If an understanding of the data is to occur an elementary approach must be taken. If all of the 705 final exam scores are averaged we can see that the average score is 28.51 with is anything but impressive. The box plot below shows the Min, Q1,median, Q3 and the Max Figure 2.0 4.0Bivariate Analysis

This section will discuss the possible factures that may have an effect on the student’s exam results. The following factors and there impacts will be analysed, they are the gender of the student, wither or not the student is in a double degree, there quiz results and there report grade. Let’s begin. 4.1Gender

It can be seen from the data that there is at best a marginal difference in the way that gender affects the final exam results. The covariance between the too only varies from 0.16 to 0.11 the difference is less than one therefore it is seen as insignificant.

Figure 3.0

The difference in the distribution seen here has no impact on the final exam results therefore the next factor will be analysis in on the next page.

4.2Double Degree

The impact of whether or not the student is taking a double or single degree offers some helpful insight for the first time in this report this report about what if anything is influencing the student’s final exams.

Figure 4.0

The graph above shows a noticeable difference in the exam outcomes between the two groups. The students what where enrolled in a double degree scored somewhat higher than the students that where only undertaking one degree. This may be to the fact that they are more focused and probably not working full time or even part time. We will continue our analysis on the following pages by looking at academic factors within BSB123.

4.3Quiz Results

Analysing the effect that the weekly quiz results have on the final exam results can help to understand if high quiz results mean high exam results. Figure 5.0

The data in the above scatter plot shows that there is a correlation between the quiz results and the exam results. R² = 0.536, which indicates that about 54% of the variation in the average of the quiz is accounted for the linear relationship with the exam results. In other words, about 46% of the variation is not explained by the least-squares regression line.

4.4Report Results

The last exam factor that will be addressed in the bivariate section is the impact of the results from the mid semester report on the exam results.

Figure 6.0

The correlation between the report results and the final exam results in not over whelming storage. The trend line in the graph can be seen as slopping upward from left to right showing that. It can be seen that the majority of students that achieved well on the report also achieved well on the exam

5.0Trivariate analysis

Trivariate analysis compares tree factors against each other in order to help better understand the exam out comes. 5.1 Degree vs. Exam & Quiz

Figure 7.0

Figure 7.0 states that students who are doing a double degree achieve higher marks compared to the students who are doing a single degree. On average it can be seen that over all quiz results do not have a significant impact on the outcome of students final exam results, on the other it can be seen that double degree students outperform other students at an average of 4.61%. Correlation for single degree student are 0.514 which is 51% of the variation compared to correlation of double degree students are 0.578 which is 58% of the variation. Further information relating to this discussion can be found in the appendix labelled figure 2.0.

6.0 Conclusion

After the brief analysis of the exam results it can be seen that some of the factors discussed do impact the exam results while others do not. The data set was seen as having a right skewed distribution with no outliers. Gender appeared to have no impact on the exam results. Students in a double degree average a score of 4.61% higher than other students. Quiz results showed a good indication of what a student’s exam results would be. The report results had almost no bearing on exam results. This report although brief has offered some insight into what factors impact final exam results for student’s studying BSB123.

References

Beaty, D. & Barling, J.(1982) Positive exam results—Without stress Retrieved from: http://www.sciencedirect.com.ezp01.library.qut.edu.au

Baragona,R, Battaglia, F, and Poli, I. (2011). Evolutionary Statistical Procedures: Statistics and Computing, (pp 159-197). Retrieved from: http://link.springer.com .ezp01.library.qut.edu.au