Data Analysis Research Report

Published: 2021-06-22 15:35:09
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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
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 ≤ 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.









1

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