Running Head: Descriptive Statistics ✓ Solved

Running Head Descriptive Statistics

Descriptive statistics Descriptive statistics is a branch of statistics that use mathematical knowledge to describe basic features of data (Miller & Chambers, 2013). These basic features include measures of central tendency and measures of variation. For this research paper, we are using the longitudinal student to describe how descriptive statistics analysis is carried out. The two variables used in the data set is the number of AP sciences courses offered in schools and the number of AP mathematical courses offered in schools. Table 1: Descriptive Statistics Summary Output Descriptive Statistics N Range Mean Std. Deviation Variance Skewness Kurtosis Statistic Statistic Statistic Std. Error Statistic Statistic Statistic Std. Error Statistic Std. Error Number of AP science courses offered ........038 Number of AP math courses offered ........038 Valid N (listwise) 16545 Table 1 shows a summary of descriptive statistics output for two variables namely number of AP science courses offered in schools and the number of AP mathematics courses offered in schools. From the analysis, the average number of AP science courses offered in a school is 2.39 with a standard error of 0.012 (Uda & Abe, 2016). The average number of AP mathematics courses offered in a single school is 1.83 with a standard error of 0.007. The variance for the number of AP sciences courses offered in a school is 2.302 while that of AP mathematical courses offered in schools is 0.940. The range between in the number of AP science courses offered in schools is given as 6 while the range for the number of AP mathematical courses offered in schools is given as 4.The implications to social change according to the results show that schools in this area offer more AP science courses as compared to the AP mathematical courses that are offered in the same schools. This information can be used to inform changes in education policy. References Miller, A. and Chambers, D. (2013).Descriptive Analysis of Flavor Characteristics for Black Walnut Cultivars. Journal of Food Science , 78(6), pp.S887-S893. Uda, T. and Abe, T. (2016).A Descriptive Statistics on Coworking Spaces in Japan. SSRN Electronic Journal . OSH 200 Measurement of Safety Performance Math and Stats Fundamentals Why sound math skills for safety performance measurement? Measurements / metrics should be reliable and accurate Collected data must be analyzed Useful comparisons between results and goals Determine trends / changes Validate controls Validate analysis methods Reliable forecasting Data Formats Categorical Data Categories (i.e., male / female; departments, etc.) Ordinal Data Survey Data Likert Scales Interval Data Ratio Data Categorical Data Categories (i.e., male / female; departments, etc.) Only differentiate membership in a group Least useful from statistical analysis standpoint Ordinal Data “order†/ “orderingâ€; Survey Data (i.e. Likert Scales); No value comparisons More useful statistically than categorical, but low Interval Data Continuous / continuous scale; Equality between points on the scale; Zero is simply a “place holderâ€; Fair degree of flexibility; Example: Fahrenheit / Celsius thermometer; More statistically useful than categorical and ordinal Ratio Data Continuous data; Zero is not simply a placeholder (represents the absence of a characteristic); Magnitude between values exist; Counting number of instances; Highest degree of statistical usefulness Descriptive Statistics Population Data Measures of Central Tendency Mean Median Mode Measures of Variability Range Variance Standard Deviation Correlation Coefficient Inferential Statistics Sample Data Statistics that Allow for an Inference Sampling Distribution Differences between Means Chi Square Mean Mean = Σ X N Σ X = sum of the individual items / observations / values N = total number of individual items / observations / values Median Point where 50% of the values lie above and 50% of the values lie below First arrange values / items from lowest to highest If odd # of values / items, then median is the “middle†value / item If even # of values / items, then average the two “middle†values / items Mode Most Frequently Occurring # There may be more than one mode in a set of data Range Difference between the lowest value and the highest value in the distribution Arrange from lowest to highest; subtract lowest from highest Variance for Samples σ² = Σ (x-mean)² + (y-mean)² N-1 N= total number of observation Variance for Total Population σ² = Σ (x-mean)² + (y-mean)² N N= total number of observation Standard Deviation √σ² Standard Deviation = √ Σ (v1 – mean)² + (v2-mean)²…. (n -1) Calculate Std. Deviation If entire population sample Normal Distribution N = 4 (1-p) S² p N= Total Number of Observations / Samples p= % safe / % unsafe observed S= Desired Level of Accuracy 95% Confidence Level – Two Std. Deviations from Mean UCL LCL MEAN Chart1 J F M A M J J A S O N D Month # of Accidents Monthly Accident Control Chart Sheet1 J F M A M J J A S O N D Sheet1 Month # of Accidents Monthly Accident Control Chart Sheet2 Sheet3 UCL / LCL Calculations for #s of Events / Samples 95% Statistical Significance = 2 std. deviations from mean = 1.96 = normal distribution UCL = X + ZS LCL = x – ZS X = mean Z = normal distribution (in safety use 1.96) S= Std. Deviation of Population 95% Statistical Significance = 2 std. deviations from mean = 1.96 = normal distribution UCL = p + 1.96[p(1-p)/n]ˆ0.5 LCL = p - 1.96[p(1-p)/n]ˆ0.5 p= mean proportion / % UCL / LCL Calculations for Proportions / % Standard Deviation = √ Σ (v1 – mean)² + (v2-mean)²…. (n -1) Calculate Std. Deviation If entire population sample * Monthly Accident Control Chart Month # of Accidents Series JFMAMJJASOND OSH 200 –Measures of Safety Performance Assignment Four XYZ Corp.’s # of Management Safety Walks By Month and Corresponding # of Recordables Month / Year # of Walks #Recordables Jan Feb March April May June July August September October November December Jan Feb March April May June July August Sept Oct Nov Dec . Calculate the following for each set (column) of data: a. Mean b. Median c. Mode d. Range e. Standard Deviation 2. Calculate the correlation coefficient between # of recordables and # of management walks. 3. Construct statistical process control chart for each set of data. 4. Can you reach any conclusions about the effectiveness of management walks? 5. What might you do further statistically investigate the effectiveness of management walks? STUDY VARIABLE 3 The two diagrams here represent two different data where the associate degree data is continuous variable while the high school data is categorical. The categorical data set represent the continuous data set is the kind data that has two extremities while categorical data is infinite (Smithson & Merkle, 2013). From the data there is the general realization that is high school students have not yet made up made up their minds as to the career paths they will take once they finish school. However, students in the university pursuing associated degree are assertive and have made up their minds of their respective career paths. When it comes to other factors such as proficiency in class, high students are free spirited and not as worried of their grades as students pursuing associate degrees (Rumrill, 2015). The reason for such an observation is that high school students have not matured emotionally, socially and intellectually. Furthermore, they still have numerous opportunities in life to make mistakes but still catch up. However, individuals pursuing their associate degrees are assertive in the knowledge that if they make any mistakes they mind end up being thrown out of campus and that would be the end of their career. Furthermore, they do not have many window years to mess around because everybody expects them to settle in their careers and begin being productive to their families and to the nations (Hoy, 2010). Therefore, it is important for the two groups they represent different types of data. These two variables collected from longitudinal studies demonstrate how the same physical data can demonstrate different migrations when statistical tools of analysis are employed. Therefore, it is important for researchers to put these factors into perspective especially when conducting studies. References Hoy, W. K. (2010). Quantitative Research in Education. Washington, DC: Sage. Rumrill, P. D. (2015). Research in Special Education. New York, NY: Wiley. Smithson, M., & Merkle, E. C. (2013). Generalized Linear Models for Categorical and Continuous Limited Dependent Variables. Los Angeles, CA: CRC Press.

Sample Paper For Above instruction

In this paper, we explore descriptive statistics with a focus on two specific variables: the number of Advanced Placement (AP) science courses and the number of AP mathematics courses offered in schools. Using a dataset of 16,545 observations, we analyze the central tendencies, variability, and distribution characteristics of these variables, illustrating how descriptive statistics can inform educational policies and social changes.

Introduction to Descriptive Statistics

Descriptive statistics involve summarizing and organizing data to highlight key features, making complex data more accessible and understandable (Miller & Chambers, 2013). It uses measures of central tendency such as mean, median, and mode, in addition to measures of variability like range, variance, and standard deviation. Understanding these aspects helps illustrate the profile of a dataset and facilitate decision-making processes, particularly in educational settings.

Analysis of AP Courses Data

The dataset under review contains two main variables: the number of AP science courses and AP math courses offered per school. The analysis begins with calculating measures of central tendency. The average number of AP science courses offered in a school is 2.39, with a standard error of 0.012, indicating a relatively consistent offering pattern across schools. In contrast, the average number of AP math courses is slightly lower at 1.83 with a standard error of 0.007, suggesting less emphasis on mathematics compared to sciences in these schools (Uda & Abe, 2016).

The variance for AP sciences courses is calculated at 2.302, indicating variability in course offerings among schools, while the variance for AP math courses is smaller at 0.940, reflecting less variability in math offerings. The range, which measures the spread between the lowest and highest number of courses, is 6 for sciences and 4 for mathematics, indicating a broader variation in science course offerings. These statistics help understand the distribution and spread of course offerings across different schools, providing insights for targeted policy interventions.

Implications for Policy and Social Change

The data suggest that schools tend to prioritize science courses over mathematics, which could influence future student interest and career pathways. Educational policymakers can leverage these insights to promote a more balanced curriculum, encouraging increased math offerings to align with STEM (Science, Technology, Engineering, and Mathematics) initiatives. As science and math skills are critical in a technology-driven economy, enhancing math course availability could improve competitiveness and innovation capacity at the national level.

Further Statistical Investigations

While descriptive statistics offer valuable insights, further inferential analyses could deepen understanding. For example, conducting correlation studies between the number of AP science and math courses might reveal if schools emphasizing one tend to neglect the other or if efforts to increase offerings in one domain influence the other negatively or positively. Additionally, employing hypothesis tests such as t-tests or ANOVA could determine if differences in course offerings are statistically significant across various school types or regions, guiding resource allocation effectively.

Constructing control charts for course offerings across regions or over time can help monitor trends and detect shifts that might signal policy impacts or curricular reforms. These tools assist in ongoing quality assurance and facilitate data-driven decision-making, essential for dynamic educational environments.

Conclusion

In summary, descriptive statistics provide a foundational understanding of educational data, revealing disparities and opportunities for policy improvement. The analysis of AP course offerings demonstrates the utility of statistical measures in portraying data distributions and variability. Further investigations, including inferential testing and trend analysis, can enhance decision-making efforts aimed at fostering equitable and comprehensive education systems.

References

• Miller, A., & Chambers, D. (2013). Descriptive Analysis of Flavor Characteristics for Black Walnut Cultivars. Journal of Food Science, 78(6), S887–S893.
• Uda, T., & Abe, T. (2016). A Descriptive Statistics on Coworking Spaces in Japan. SSRN Electronic Journal.
• Hoy, W. K. (2010). Quantitative Research in Education. Sage Publications.
• Rumrill, P. D. (2015). Research in Special Education. Wiley.
• Smithson, M., & Merkle, E. C. (2013). Generalized Linear Models for Categorical and Continuous Limited Dependent Variables. CRC Press.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.
• Moore, D. S., & McCabe, G. P. (2014). Introduction to the Practice of Statistics. W.H. Freeman.
• Levine, D. M., Stephan, D. F., Krehbiel, T. C., & Berenson, M. L. (2015). Statistics for Managers Using Microsoft Excel. Pearson.
• Corning, T., & Hesketh, F. (2018). Data Analysis and Decision Making. Wiley.