Data Analysis Research Report

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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.

Examination Results

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 &lt; 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

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

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

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

7,584.65816

Percentile 25% (Q1)

12.

Geometric Mean

13.29844

Percentile 75% (Q3)

16.

Harmonic Mean

12.8176

IQR

4.

Mode

14.

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

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.