RSCH 7864 Assessment 1: Descriptive Statistic
Descriptive Statistics
Descriptive statistics are a concise summary of the collected data, giving information about central tendencies, variability, and the overall score distribution. In this case, the performance of students is measured using GPA and Quiz 3 scores. The important statistical indicators in this case are mean, standard deviation, skewness, and kurtosis, which help in determining the fairness and consistency of the results. RSCH 7864 Assessment 1: Descriptive Statistic These metrics reveal the patterns that occur in the student’s performance at different levels of class. This detailed analysis would point to the reliability of the assessments and prevent differences in scores from being too high and outside acceptable margins.
Histograms for Visual Interpretation
Distribution Plots
Final
Lower-division
Upper-division
The histograms vividly depict the academic performance data for students that are lower-division freshmen and sophomores as well as the upper-division students, juniors, and seniors, of which all have about 40 students within the group focusing on their respective scores for the same test. Lower-division students had 40 to 75, whereas the upper-division students ranged widely from 30 to 75. The average score of lower-division students was at 60; however, their upper-division counterparts showed an average score to be at a slightly higher average of 60.554. This shows the minimal variation of average scores indicates a relatively fair similarity in performance overall between the groups.
For both lower-division and upper-division students, the middle tendency is 62 indicating equal distribution to a midpoint but for the variability, it is the standard deviation between two groups wherein lower-division students have a standard deviation to the value of 5.983 with a relatively close scores distribution as against for upper-division the standard deviation at 8.592 level depicting the significant degree of more variability or spreading scores. The histogram of the lower division is more narrow and appears more normal in comparison, showing students performed relatively consistently. In comparison, the upper-division histogram is a bit skewed with its scores spread over a larger range, which denotes greater variability amongst those students.
A close examination of the two groups reveals that, although the upper-division students scored on average a little higher, some were overwhelmed by the rigor of advanced coursework, as their scores indicate at the lower end. The scores of the lower-division students were much more uniform, centered in the middle range, as one would expect for foundational-level coursework. The histograms indicated that the examination was fair since it fairly evaluated the capabilities of students in both divisions with a minimal difference in central tendency and variability. The results call for the implementation of academic support to help with the unique challenges posed at different academic levels.
Measures of Central Tendency and Dispersion
| Descriptive Statistics | |||||
|---|---|---|---|---|---|
| GPA | Quiz3 | ||||
| Mean | 2.864 | 4.962 | |||
| Std. Deviation | 0.692 | 1.550 | |||
| Skewness | -0.096 | -0.093 | |||
| Std. Error of Skewness | 0.236 | 0.236 | |||
| Kurtosis | -0.832 | -0.034 | |||
| Std. Error of Kurtosis | 0.467 | 0.467 | |||
The information list shows the statistical values of GPAs and Quiz 3 scores for a class of students, where there are both lower and upper-division students, as in the previous example. The average GPA is 2.864, with the mean for Quiz 3 at 4.962; this latter value reflects an overall good score for students. The GPA has a standard deviation of 0.692 indicating moderate variability between the grades while the standard deviation for Quiz 3 is at 1.550, reflecting more variability within the quizzes relative to the GPAs. That means students are fairly consistent about their grades compared to Quiz 3, with more variability involved.
From the score distributions, skewness values for both GPA (-0.096) and Quiz 3 (-0.093) are nearly close to zero. This indicates that data have nearly symmetry with no skew to either side. Furthermore, the standard error of skewness for the two variables is 0.236. This further justifies the observation made about minimal skewness. The kurtosis for GPA is -0.832, and for Quiz 3, it is -0.034. Such negatives signifying relatively flat distributions with fewer outliers based on extreme values than the case of a normal distribution indicate that the standard error of kurtosis is within an acceptable range at 0.467. GPA and Quiz 3 show balances and consistencies in their measures with no occurrence of significant deviations from a normal distribution. The fairness of the measurement process is evident across student groups, regardless of class level. Both skewness and kurtosis values are within the range of -1 to +1, which reflects symmetry and appropriate peak levels. Moreover, the standard errors for skewness and kurtosis are within the range of -2 to +2, which confirms that any deviations from normality are minimal and well within acceptable limits.
Conclusion
In summary, the given descriptive statistics give an overview of students’ performance at all class levels. Central tendency, dispersion, skewness, and kurtosis from the analysis all show minimal variability, and distribution is acceptable for both GPA and Quiz 3 scores. The closeness between the means, medians, and standard deviations gives a fair implication that the assessment was unbiased. Additionally, the skewness and kurtosis values support that the data is normally distributed with no outliers. In summary, the statistical analysis shows that the test does measure the student performance of the lower-division and upper-division groups both validly and reliably.
