Data Analysis Research Report

Title of Assessment: Data Analysis Research Report

Introduction

The final examination is a critical assessment as it composes 60% of overall assessments in the course. It is therefore vital to determine which factor influences the exam performances of the students. The purpose of the research is to be able to determine if there are factors, among considered in this research, have an influence on students’ examination results. If findings are significant, it can be used to predict patterns of these factors and may be able to assist in structuring the course in a way that will allow students to achieve best possible outcomes.

Method

The sample for this study was 705 students who took BSB123 at Queensland University of Technology. Data collected on this research includes: gender, number of degrees, and their assessments results in BSB123. Summary charts of data collected are provided in the Appendix. All calculations and charts were done in Excel, to minimise human error. However, the research may provide limited information, as factors measured were limited.

BSB123 Examination Results
Count 705 Skewness 0.46042
Mean 28.51645 Mode 20.
Variance 153.66785 Coefficient of Variation 0.43471
Standard Deviation 12.39628 Mean Deviation 10.14061
Minimum 5. Median 26.5
Maximum 59. Median Error 0.02204
Range 54. Percentile 25% (Q1) 19.5
Sum 20,104.1 Percentile 75% (Q3) 36.875
Sum Standard Error 329.1441 IQR 17.375
Total Sum Squares 681,479.81 MAD 8.

Analysis

Examination Results

Figure 1. Descriptive Statistics Table (extract)

Figure 2. Distribution of BSB123 Exam Results

There is much information that can be gathered just by looking at the histogram. First, it shows how data are distributed. Second, the modal interval or most frequent marks the students received were 20-25. Last, it shows the shape of the data, which have a slight skew to the right. Figure 1, provides more detailed calculations for the data set. First, it shows that the mode is 20, which agrees to the histogram. Second, it provides the mean and median, which are 28.51645 and 26.5 respectively. This supports the histogram that there is a slight skew on the right, since mean is greater than the median but not by much. Meaning, most students’ got marks below the median. However it is slightly pulled up by some higher marks, which makes the average slightly greater than the middle score. In this case, the data was checked for outliers to ensure that the mean was not abnormally affected by an extreme value. It was found out that the highest and lowest standard scores are 2.45908745 and -1.897056742 respectively. Neither of which is considered an outlier and therefore the mean is a reliable measure of central tendency. Lastly, Figure 1 gives us the Inter Quartile Range (IQR), which provides a robust measure of dispersion since it is not affected by outliers. Given that the IQR is 17.375, the data are quite dispersed since the IQR or middle 50% of the data is relatively small compared to the Range that is 54. In the following graphs, it will be explained whether there are any of the other factors collected have an influence over the exam results. A table of coefficient of correlation, and sample covariance is provided below and will be used to discuss the linear relationship between variates.

Figure 3. Coefficient of Correlation and Sample Covariance

CORRELATION R² COVARIANCE
QUIZ – EXAM 0.53645469 0.287783635 22.55628546
Single Degree 0.514820061 0.265039695 21.82571032
Females 0.425786454 0.181294104 16.30120052
Males 0.583767491 0.340784483 27.02006961
Double Degree 0.578089177 0.334187097 22.50394623
Females 0.607654528 0.369244026 23.80332634
Males 0.515221913 0.265453619 19.09510926
REPORT – EXAM 0.292805681 0.085735167 11.91386535
Single Degree 0.245318119 0.06018098 10.0141343
Females 0.225212514 0.050720677 7.711304064
Males 0.267650839 0.071636972 12.32651487
Double Degree 0.326278023 0.106457349 11.85340249
Females 0.359306148 0.129100908 12.69093497
Males 0.250645118 0.062822975 9.04393424

Exam to Report Results

Figure 4. Exam to Report Results Chart

There is a positive relationship between the exam and report results as their covariance is 11.91386535. This means as the report results increases, the exam result increases too. However, the strength of the relationship should be considered, which is given by the coefficient of correlation. Given the coefficient of correlation is 0.292805681; it is considered a weak relationship since it belongs under 0 ≤ r < 0.3. This is easily seen in the graph. The data points are scattered away from the line of best fit, which shows there is a weak relationship between exam results and report results.

Figure 5. Exam to Report Results – Single Degree

Concentrating on the exam and report results of single degree students, it can be analysed through the graph. It shows that there is also a positive relationship between the two results for both genders. Also, with the data points scattered, it can be analysed as a weak relationship for both genders. This is supported by their coefficient of correlation: 0.225212514 for females, 0.267650839 for males, and 0.245318119 for all single degree students. These are all considered weak relationship as it is also under 0 ≤ r ≤ 0.3.

Figure 6. Exam to Report Results – Double Degree

It can be seen in the graph that there is a positive relationship as well. However, there is a recognisable difference between the slope of line of best fit of males and females. It is evident on their covariance: males have 9.04393424, while females have 12.69093497. This will also reflect on their coefficient of correlation in which females have 0.359306148, while males have 0.250645118. It shows that being a female doing a double degree have a higher relationship between their report and exam results. Although, it is still considered a moderate relationship as it belongs under 0.3 ≤ r ≤ 0.7.

Exam to Quiz Results

Figure 7. Exam to Quiz Results Chart

As seen on the graph the quiz results and exam results have a positive linear relationship as the direction of the line of best fit is going upwards. This is also supported by the covariance 22.55628546. To determine the strength of this relationship, coefficient of correlation is calculated and given as 0.53645469. Although, this is the highest correlation so far, this is still considered as a moderate relationship. Following are the breakdown of relationship of exam and quiz results by number of degrees and gender.

Figure 8. Exam to Quiz Results – Single Degree

As the graph shows, there is also a positive relationship between the results of students doing a single degree. It can also be seen that the linear relationship of males are steeper than females. This is reflected through their covariance with males as 27.02006961, and females as 16.30120052. Then use the coefficient of correlation to determine the strength of the relationship. Males have 0.583767491, and females have 0.425786454. Even though males have a higher coefficient of correlation, the relationship between the exam and quiz results of both genders are considered a moderate relationship.

Figure 9. Exam to Quiz Results – Double Degree

From the graph, it can be said that there is a positive relationship between the quiz results and exam results of both genders doing double degree. To prove this, the sample covariance was given: males with 19.09510926, and females with 23.80332634. It is apparent that female covariance is greater than the male covariance. These values will give an indication that the coefficient of correlation of females would also be greater than of the males’. As calculated, females have 0.607654528, while males have 0.515221913. Although the coefficient of correlation for females is higher, both are still considered to have moderate relationship between their quiz and exam results.

Conclusion

In conclusion, both report and quiz results have a positive relationship with the exam results. However, the quiz results showed a stronger relationship to the exam results than the report results. The report results have a weak relationship with the exam results, with only the exception of females doing double degree having a moderate relationship between their results. On the other hand, the quiz results have a moderate relationship with the exam results. Unfortunately, there is no relationship to be considered significant to be a basis for predicting the exam results. Appendix

Respondents

Quiz Results Chart

Report Results Chart

Descriptive Statistics Tables

Quiz Results

Count 705 Skewness -1.01846
Mean 15.22199 Skewness Standard Error 0.09193
Mean LCL 14.92413 Kurtosis 4.22775
Mean UCL 15.51985 Kurtosis Standard Error 0.18307
Variance 11.50498 Alternative Skewness (Fisher’s) -1.02063
Standard Deviation 3.3919 Alternative Kurtosis (Fisher’s) 1.24506
Mean Standard Error 0.12775 Coefficient of Variation 0.22283
Minimum 0.E+0 Mean Deviation 2.70997
Maximum 20. Second Moment 11.48867
Range 20. Third Moment -39.6596
Sum 10,731.5 Fourth Moment 558.01774
Sum Standard Error 90.06117 Median 16.
Total Sum Squares 171,454.25 Median Error 0.00603
Adjusted Sum Squares 8,099.50922 Percentile 25% (Q1) 13.
Geometric Mean 14.69729 Percentile 75% (Q3) 17.5
Harmonic Mean 14.00011 IQR 4.5
Mode #N/A MAD 2.

Report Results

Count 705 Skewness -0.98384
Mean 13.85248 Skewness Standard Error 0.09193
Mean LCL 13.56424 Kurtosis 4.52728
Mean UCL 14.14072 Kurtosis Standard Error 0.18307
Variance 10.77366 Alternative Skewness (Fisher’s) -0.98594
Standard Deviation 3.28233 Alternative Kurtosis (Fisher’s) 1.54673
Mean Standard Error 0.12362 Coefficient of Variation 0.23695
Minimum 0.E+0 Mean Deviation 2.49031
Maximum 20. Second Moment 10.75838
Range 20. Third Moment -34.71719
Sum 9,766. Fourth Moment 523.99999
Sum Standard Error 87.15177 Median 14.
Total Sum Squares 142,868. Median Error 0.00584
Adjusted Sum Squares 7,584.65816 Percentile 25% (Q1) 12.
Geometric Mean 13.29844 Percentile 75% (Q3) 16.
Harmonic Mean 12.8176 IQR 4.
Mode 14. MAD 2.

Exam Results

Count 705 Skewness 0.46042
Mean 28.51645 Skewness Standard Error 0.09193
Mean LCL 27.42787 Kurtosis 2.50864
Mean UCL 29.60504 Kurtosis Standard Error 0.18307
Variance 153.66785 Alternative Skewness (Fisher’s) 0.4614
Standard Deviation 12.39628 Alternative Kurtosis (Fisher’s) -0.4863
Mean Standard Error 0.46687 Coefficient of Variation 0.43471
Minimum 5. Mean Deviation 10.14061
Maximum 59. Second Moment 153.44989
Range 54. Third Moment 875.192
Sum 20,104.1 Fourth Moment 59,070.61064
Sum Standard Error 329.1441 Median 26.5
Total Sum Squares 681,479.81 Median Error 0.02204
Adjusted Sum Squares 108,182.16913 Percentile 25% (Q1) 19.5
Geometric Mean 25.65771 Percentile 75% (Q3) 36.875
Harmonic Mean 22.55482 IQR 17.375
Mode 20. MAD 8.

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