Student name

Capella University

RSCH-FPX 7864 Quantitative Design and Analysis

Professor Name

Submission Date

Descriptive Statistics

Part 1: Histogram

Figure 1

Lower Division

The descriptive statistics are essentially utilized to give the information that is needed by the individuals involved in data sets analysis. The statistical data enable the professionals to develop a comprehensive image of their data, and the data enable the professionals to choose the right methods of analysis to continue their practice (Fanelli et al., 2022). Data dissemination is a significant idea that can be used to make efficient decisions in the context of educational evaluation and research (Ríos et al., 2025). The specified histogram indicates the distribution of the final examination marks of the learners of the lower division. The independent variable in this representation is the last examination score, and the dependent variable is the lower division. The 5-point intervals measure the performance of the students in the range of 40-75. Such a scoring system is beneficial in giving a systematic evaluation of the academic performance of students in the course. The frequency distribution applied in the histogram enables the determination of the number of students who scored in specific areas. The highest frequency was 60-65, and it indicates the highest number of 13 students attending the highest frequency in the distribution given. Distribution is skewed to the negative, whereby we see that the tail on the lower part is longer than the tail on the higher part, hence demonstrating that more students were found to score lower than the median (around 60) than the students who scored higher. The pattern of histogram analysis shows the left-skewed form of data distribution in which most data is concentrated on the higher scores and the distribution at the lower scores.

Figure 2

Upper Division

The histogram indicates that the score range was 30 to 80 with intervals of 5. Each bar in the histogram represents the number of times the students in the upper division scored on the final examination. The histogram will show two variables, and in this case, the last will be the independent variable, but the upper division will be the dependent variable. The scales are applied to determine the performance of students, and in this case, varying levels of performance can be measured. A frequency distribution can be used to establish the number of students in particular score ranges, as the histogram below. The maximum is in the range of 65-70, and the number of students in this range is approximately 14 out of the total population of 56 respondents. The histogram frequency test indicates the bell shape, and the points are evenly distributed at both ends, in terms of the highest and lowest range. The secondary indication that the data conform to the properties of normal distribution is that the histogram has a symmetrical bell-shaped curve.

Part 02: Descriptive Statistics

Table 1

Descriptive Statistics

Mean, skewness, kurtosis, and standard deviation are the basic descriptive statistics that are used to determine the distribution and central nature of data. The skewness distribution is the measure of the alignment of the data placement by determining the concentration of the data on one hand or the other (Schmoch, 2020). The kurtosis is an evaluation of the difference between the tail of the distribution and the normal curves in terms of the thin or thick ends and height of the peaks (Kenton, 2024).

The margin between the means and the standard deviation is small, and therefore, the data is compact or rather limited to a small set of values, whereas a large gap means that the data is widely distributed or even spread. The GPA variable shows the means and standard deviation of the mean of M = 2.864 and SD = 0.692, respectively. High concentration and high central tendency are indicated in the calculations of the sum of mean and standard deviation (2.864+0.692=3.556) to find the upper limit of the GPA. The values of mean and standard deviation of Quiz 3 variable are equal to M = 6.943 and SD = 1.604, respectively. After the computation of the upper threshold of Quiz 3: (6.943+1.604=8.547), it can be seen that the data is concentrated and the centrality is significant.

The measures of skew and kurtosis are also given in descriptive statistics to test the normality of the distribution. By the values of skew and kurtosis, the values of skewness and kurtosis in the GPA variable are -0.096 and -0.832, respectively. The skew and kurtosis in the Quiz 3 are -0.333 and 0.662, respectively, and the values fall within the reasonable parameters of normality of -2 to +2. As demonstrated in the interpretation of the descriptive analysis, skewness and kurtosis variables (indicators) have been in the acceptable range (-2 up to +2) and reflect the data bearing the characteristics of a normal distribution.

Conclusion

The statistical analysis has shown that there were similar trends in the performance of upper-division and lower-division student groups. There was moderate negative skew in the data of the lower division, and the upper division had a similar normal curve distribution. The central tendency and dispersion measures were employed to indicate that the groups were centralized, and the variance was insignificant. Distribution characteristics were kept within normal ranges, and this showed that there was similarity of characteristics in the data. Generally, the findings showed uniformity in the qualities of scholastic performance and the trends in performance among the students.