- RSCH FPX 7864 Assessment 1 Descriptive Statistics.
Descriptive Statistics
Capella University
RSCH-FPX7864
Instructor Name
Due Date
Descriptive Statistics
Figure 1
Descriptive Statistics
Descriptive statistics define the difference in divergence between the upper division and lower division based on central values, such as standard deviation, mean, and data range. The upper division had a mean of M = 62.161, which was slightly higher than the mean of the lower division of M = 61.469. The lower division also recorded a higher standard deviation (SD = 8.595), signifying higher variability in the scores. The upper division, on the other hand, exhibits a higher consistency in terms of standard deviation (SD = 6.747), indicating greater consistency among the values (Cooksey, 2020). The range of all the data obtained is 40 to 75, which is representative of the whole range of values obtained. The comparison verifies that, while the highest division has a slightly higher average score, the lowest division exhibits greater variation in scores, indicating a more diverse distribution of values.
Figure 2
Lower Division
The histogram illustrates the distribution of final exam scores in lower-division courses for a sample of 49 students, along with their reported scores. The scores (40 to 75) have been grouped into 5-point classes to provide a more precise definition of the score distribution. The top was 60-65, and the distribution is as follows: two students have obtained 40-45 marks, three students have obtained 45-50 marks, eight students have obtained 50-55 marks, seven students have obtained 55-60 marks, twelve students have obtained 60-65 marks, seven students have obtained 65-70 marks, and ten students have obtained 70-75 marks. The direction of the information is to have a left-skewed distribution, where a longer tail on the left end of the chart is used to indicate that the majority of students scored lower (Pajankar, 2021). Skew is the same as M = 61.469, with a mean of 62.5 and a median of 62.5, in which the median rests marginally above the mean, representing most students with higher-than-average marks and fewer with inferior marks.
Figure 3
Upper Division
The histogram is of the previous exam scores of a sample of 56 upper-level students with exam scores as the independent variable and upper-level classification as the dependent variable. The distribution is more straightforward to comprehend as scores range between 50 and 75 in steps of 5 units. Specifically, the distribution of the students’ marks is as follows: 11 in the interval 50-55, 12 in the interval 55-60, 14 in the interval 60-65, 13 in the interval 65-70, and 6 in the interval 70-75. The marks are found to be concentrated in the range 60-65, with most of the students in this group. The bell-curve histogram indicates that the scores are usually distributed in a way that the scores cluster together in the middle and form symmetrical figures at the extremes (Pajankar, 2021). The average score, M = 62.161, approximates the median of 62.5 to a high extent due to its reliability, having been calculated from a standard deviation of SD = 6.747. The coincidence is evident in the data, which is very symmetrical with minimal skewness. The histogram shows regular performance by the upper-division team, with a regular spread of examination marks around the mean mark.
Data Set Interpretation
Part 2
Figure 4
Descriptive Statistics
Interpretation of Results
Student information offers an in-depth analysis of student performance in the form of mandatory statistical measures of Mean (M), Standard Deviation (SD), GPA, and Quiz 3. Descriptive statistics encompass measures of central tendency and dispersion in students’ performance. Mean is the average mark, and standard deviation is an estimate of how spread apart the set of marks is from the mean and informs us about how spread apart the students’ performance is from the average (Darling, 2022). Descriptive statistics of the variables GPA and Quiz 3 indicate variability and distributions. The mean is M=2.862, and the standard deviation is SD=0.713 in GPA. Variance explains some variation in the range of grades for students, but does not explain extreme variation. GPA is left-skewed by -0.220 and indicates that there are higher numbers of students on the higher end of the GPA. Kurtosis of GPA is -0.688 and indicates that there are fewer extreme scores in the GPA distribution, with the scores being more concentrated around the mean. A comparison is that the Quiz 3 mean is M = 7.133, and the standard deviation is SD 1.600.
Skewness for Quiz 3 = -0.078 and is biased towards the most symmetric distribution with the least left-skewed. The least positive, least negative measure reveals that the distribution is near normal but biased towards high scores. Kurtosis for Quiz 3 = 0.149 and exhibits peaks more normal than for GPA, but more peaked. Both distributions of GPA and Quiz 3 are moderately non-normal, but more flattened and more left-skewed for GPA than for Quiz 3. The statistical summary provides the basis for interpreting the performance difference measure for both GPA and Quiz 3, and it tells us that the two variables are moderately left-skewed but less spread, with lower kurtosis for GPA than Quiz 3. The information allows us to estimate student performance’s central tendencies and variability from measures.
Skewness and Kurtosis Distribution
Kurtosis and skewness are excellent data distribution and shape measures, especially for normality. Skewness and kurtosis are the most important measures of normality of data distribution. Skewness is asymmetry, and -1 and +1 are typical values to represent symmetric-like. Kurtosis is the tail shape of the distribution, and -2 and +2 are typical values to be normal, such that data is not exhibiting extreme tail behaviors (Hatem et al., 2022). For instance, GPA skewness is -0.220, a minimal left skew. However, since the value is less than the tolerable value, the GPAs’ distribution can also be called practically symmetrical. Practically zero near-skewness is also found at Quiz 3 as -0.078, which implies a practically perfectly symmetrical distribution with practically no important skewness, i.e., points evenly distributed around the mean (Church et al., 2019). In terms of kurtosis, the mean value of GPA is -0.688, and therefore, GPA will have fewer data points clustered around the mean and fewer peaks than in a normal distribution. Data will not be centered around the mean, but similar to a normal distribution. Kurtosis for Quiz 3 is 0.149, but again, a value closer to zero indicates that the distribution is as normal as possible, with a median peak and tail-weighted distribution. As both measures of skewness and kurtosis fall within -2 and +2 limits, it is not a giant step to conclude that GPA and Quiz 3 data are almost normal. This is particularly useful for other statistical tests, especially parametric tests, as they require normality to draw accurate inferences.
