Data Analysis Research Report

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	RA²	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  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  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  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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