RSCH FPX 7864 Assessment 1 Descriptive Statistics

Descriptive Statistics

Student Name

RSCH FPX 7864 

Capella University

Prof. Name

Submission Date

Descriptive Statistics

Part 1

The test scores of students in the lower division are varied, as indicated by a very wide distribution of the test scores with standard deviation of 8.595 and mean of 61.469 points. The distribution is between 40 and 75. The histogram reveals three levels of performance which are low, average, and high achievers. The distribution of the scores is skewed to the left with a long tail on the left-hand indicating that the number of students with lower scores (below the median point 62.5) was more than the students with higher scores. The described scores confirm the left skew because the mean score of 61.469 was lower than the median value, and the maximum peak was observed in the right-hand side.

It has been shown that in the case of a low mean compared to the median, the distribution is skewed to the left, meaning that a group with lower performance has the potential to have a disproportionately impactful influence on the overall variability (Bobbitt, 2023). Performance was very diverse, but the students with a 4050 range had difficulties in achieving a good performance, and a significant portion scored high marks. Low division-level is more variable in achievement because pupils have different trends in scores.

The standard deviation (6.747) is smaller, which means that upper-division students have a more coherent distribution of scores, which is the opposite of the situation in lower-division students. The figure illustrates that students in upper-divisions have marks (scores) that are left-skewed but almost balanced in terms of distribution, although there is a taper on either sides of the scale. The data is approximately normally distributed in its bell-shape, and the scores in the central concentration take a position between the scores of 60 and the scores of 70, consecutively decreasing in the tails.

This distribution is consistent with the literature stating that the data of student performance follow a normal curve frequently (Fulk, 2023). The symmetrical tendency can also be supported by the fact that the mean and median scores are nearly the same (62.161 and 62.5, respectively), as well as the distribution across the whole population is not that skewed. The figure indicates that the performance of upper-division students was normally distributed and consistent, with the distribution having few outliers at both sides of the distribution and the majority of the results around the central values.

Data Set Interpretation

Part 2

The results of Quiz 3 revealed an average score, the mean and standard deviation measure of M= 7.133 and SD= 1.600, as the results of the analysis indicated a moderate variability, as nearly 68.3% of the scores ranged between 5.533 and 8.733. The skewness value (-0.078) showed that there was a slightly extended left tail, whereas the kurtosis value (0.149) demonstrated that the distribution was too close to normal. According to research, kurtosis and skewness can be used as crucial tools to determine the shape of the distribution and the presence of normality, with the value of +2 to -2 regarded as being satisfactory to analyse psychological and educational data (Borroni and Capitani, 2023).

The current data on GPA showed that the mean of GPA was M= 2.862 on a 4.0 scale and SD= 0.713, meaning that there was moderate variation. The skewness (−0.220) indicated a small left tail, which indicated that the distribution was clumped at the higher GPA range, as there were some low performers, whereas the skewness kurtosis was negative (−0.688) indicating a flatter distribution than normal. It is indicated that negative kurtosis indicates a lower level of extreme outliers and a more widespread level of data, which may be more accurate at the group-level central tendency (Blanks et al., 2020).

Descriptive analysis of Quiz 3 and GPA indicates that both the descriptive statistics fall within the range of (-2 to +2) which is an acceptable range of normality. The specified outcome means that the dataset has a stable and valid measure to undertake additional statistical tests, which is in line with the suggested practices of the data reliability in the educational and behavioral research.

Conclusion

Descriptive statistics analysis showed that there were significant differences in performance by lower- and upper-division students. Scores in lower directions were more skewed and variable with groups of low, average, and high achievers, whereas in the upper divisions, the scores were consistent and exhibited almost a normal score. The outcomes of Quiz 3 showed a slight variability of the scores, and the distribution was rather close to normal, with the majority of the learners performing an average score. GPA analysis also indicated moderate variation, slight left skew, and negative kurtosis, indicating that higher achievers are clustered around, in addition to low achievers.