RSCH FPX 7864 Assessment 1 Descriptive Statistics

The main objective of this assessment is to demonstrate student performance analysis through descriptive statistics by applying JASP software. The evaluation reflects the development and analysis of two histograms to evaluate the scoring patterns for final exams between lower and upper-division students. The study determines central tendency metrics and dispersion indicators for both GPA scores and Quiz 3 results using mean, standard deviation skewness, and kurtosis values. The main objective is to gain fundamental abilities in interpreting data distributions while learning to detect variable normality (Cooksey, 2020). The obtained information is a crucial foundation for performing advanced statistical examinations.

Part 1: Histograms

According to the research findings, students display varied approaches toward histograms used for data distribution visualization (Boels et al., 2024). A summary of the “final” scores exists within the table, analyzing students from lower and upper-division groups. The upper division contains 56 students among the two groups, while the lower division contains 49 students. The final exam scores show a slight increase between lower-division students (61.469) and upper-division students (62.161), with minimal difference between the averages.

The standard deviation values show lower-division students have a more diverse score distribution than upper-division students since their dispersion reaches 8.595, while upper-division students show 6.747. The scores obtained by lower division students display greater variability with score ranges between 40 to 75. In comparison, the upper-division students scored from 50 to 74, which suggests significantly lower scores and more variability among lower-division students. The histograms show the distribution of final scores for both groups:

• X-axis: Final scores (ranging from 40 to 75).
• Y-axis: Counts (number of students with scores in each bin).

RSCH FPX 7864 Assessment 1 Descriptive Statistics

Lower division students’ scores reveal a wide distribution across the range because their standard deviation measures 8.595. The data points shift to the left side while showing concentration between the lower scoring 40-50 marks. Most lower-division students scored between 55–60 according to the peak of the distribution. The frequency distribution extends widely because students obtained scores ranging from 40 to 75 points. The scoring patterns among lower division students show three performance levels because they include poorly performing and highly performing students and those who earn average scores. Data points between 40–50 points show substantial difficulty for students, yet the distribution extends to 75, showing that many students achieved excellent results. 

The histogram representing upper-division students displays a higher concentration of scores, corresponding to their reduced standard deviation value of 6.747. Most student scores (62.161) cluster within a tightly packed distribution ranging from the mean to the left since no students received scores under 50. The scores cluster near 60–65 since approximately 14 students recorded their results in this same range. The distribution shows slight left-tailed skewness, although it maintains more balance than the lower division results. The scores taper off gradually on both ends, with fewer students scoring in the 50–55 and 70–75 ranges. Most upper-division students maintained a 60–65 rating scale, scoring fewer points below 50 or above 65 than lower-division students.

Comparative Insights

The performance consistency of upper-division students becomes higher since their grades demonstrate strong cluster distribution closely related to the mean and narrow standard deviation. Lower division-level education shows greater performance variability because students maintain diverse score patterns. Low scores among lower-division students reach a minimum of 40. Still, upper-division students maintain grades above 50, indicating superior foundational knowledge or improved preparation. High-Achieving Students in the lower division reach marks between 70–75, while the upper division achieves identically yet stops at 75 (lower division) versus 74 (upper division). The upper division contains more students who achieve scores between 60–65 points than the lower division, although the peak of their score distribution remains at 60–65 points.

Part 2: Descriptive Statistics

GPA

The mean GPA stands at 2.862 points and corresponds to a B- grade based on the 4.0 scale (a B grade equals 3.0 points). The students perform below the average GPA range when using 3.0 as the benchmark. The standard Deviation stands at 0.713 to indicate how GPA scores disperse from the mean value. GPAs display moderate differences between students based on the value of 0.713. The typical GPA distribution matches the “C+” grading level while also including “B+” grades as students’ scores lie between 2.149 and 3.575 (mean ± 1 standard deviation).

Quiz3

Most students achieved 71.33% (7.133) on Quiz 3, which involved 10 points as points maximum. The students performed well, giving results similar to the middle section of traditional grades between “C” and “C+.” The standard deviation reveals the distribution of quiz scores because it amounts to 1.600. Quiz score variations show an average spread level because the standard deviation is 1.600. Most trainees earned scores ranging from 5.533 to 8.733 (mean ± 1 standard deviation), which translated from “D+” to “B+” grades.

Interpretation of Skewness and Kurtosis

Skewness: A distribution becomes asymmetric when skewness occurs. A zero value in skewness measurement indicates a symmetrical distribution similar to the normal distribution. The distribution exhibits positive skewness when it extends farther to the right side of the mean with additional high-value points in its tail. Negative skewness depicts an extended tail on the left side, with additional low-value points extending toward negative values.

We verify skewness statistical significance by comparing the computed value with its standard error threshold. The rule indicates that statistical significance in skewness is signified when the skewness absolute value exceeds its standard error value by twice the amount (Hammouri et al., 2020). The GPA distribution shows a slight right skew, meaning a few students have higher GPAs than most, but the skew is not strong enough to be considered significant. This means the GPA scores are fairly balanced and close to normal. Similarly, Quiz 3 scores have a very small left skew, with a few lower scores, but the skew is not significant. Overall, both GPA and Quiz 3 scores are close to being normally distributed and fairly symmetric.

RSCH FPX 7864 Assessment 1 Descriptive Statistics

Kurtosis: Distribution kurtosis refers to the extent of deviation between distribution shape and the normal distribution. Kurtosis statistics of 0 represent normal distribution patterns (mesokurtic). Data distribution shows positive kurtosis (leptokurtic) when it displays heavier tails combined with a more pronounced peak than a normal distribution. Still, negative kurtosis (platykurtic) indicates lighter tails with a flatter peak.

Kurtosis significance tests happen by comparing the kurtosis value with its standard error values. Kurtosis will be significant when its absolute value surpasses 2 times the standard error of kurtosis (Iacobucci et al., 2025). The GPA scores are slightly flatter than a normal distribution, meaning there are fewer very high or very low GPAs, but this difference is not big enough to be considered important. Quiz 3 scores are more peaked, with more students scoring close to the average and a few having very high or low scores. However, this small difference from a normal distribution is insignificant, as with GPA. Overall, both scores are shaped very similarly to a normal distribution.

Conclusion 

The descriptive statistics confirm that both GPA scores and Quiz 3 results demonstrate normal distribution despite minor but non-substantial deviations from normality. The upper-division students showed more uniform performance patterns than the lower-division students. The data shows that students’ average scores are spread moderately across GPA and quiz scores. All statistical data demonstrate good conditions for valid interpretation techniques.

References

Boels, L., Bakker, A., Dooren, W. V., & Drijvers, P. (2024). Secondary school students’ strategies when interpreting histograms and case-value plots: an eye-tracking study. Educational Studies in Mathematics, 118. https://doi.org/10.1007/s10649-024-10351-3 

Cooksey, R. W. (2020). Descriptive statistics for summarising data. Illustrating Statistical Procedures: Finding Meaning in Quantitative Data, 1(1), 61–139. https://doi.org/10.1007/978-981-15-2537-7_5 

Hammouri, H. M., Sabo, R. T., Alsaadawi, R., & Kheirallah, K. A. (2020). Handling skewed data: a comparison of two popular methods. Applied Sciences, 10(18), 6247. https://doi.org/10.3390/app10186247 

RSCH FPX 7864 Assessment 1 Descriptive Statistics

Iacobucci, D., Román, S., Moon, S., & Rouziès, D. (2025). A tutorial on what to do with skewness, kurtosis, and outliers: New insights to help scholars conduct and defend their research. Psychology and Marketing, 42(5), 1398–1414. https://doi.org/10.1002/mar.22187