Short Title Of Paper 1 Running Head Descriptive Statistics

Short Title Of Paper1running Head Descriptive Statistics1descriptive

Determine the appropriate descriptive statistics. Note: If the data was normally distributed, use the mean and standard deviation. If the data was skewed significantly, use the median and interquartile range. Specify the distribution, central tendency, dispersion, minimum and maximum values, and confidence interval if applicable. Create a bar chart for attribute variables; describe the proportions. Include raw data in Appendix A, charts and tables in Appendix B, and descriptive statistics in Appendix C. Provide interpretations of the descriptive statistics, explaining the results in layman's terms.

Paper For Above instruction

This paper aims to analyze and interpret the descriptive statistics of two numerical variables—body weight and age—and an attribute variable—education level—based on a sample of 100 subjects. The analysis involves determining the distribution, calculating relevant central tendency and dispersion measures, constructing appropriate visualizations, and providing straightforward interpretations of the findings.

Analysis of Body Weight

The body weight data for 100 subjects ranged from 99 pounds to 234 pounds. Before selecting the appropriate descriptive statistics, a histogram was examined to assess the distribution. The histogram indicated that body weight data approximated a normal distribution, characterized by a symmetrical shape with slight skewness, thus justifying the use of the mean and standard deviation as descriptive measures.

The mean body weight was calculated as 149 pounds, representing the average weight in the sample. The standard deviation was approximately 30 pounds, indicating a moderate variation around the mean. The minimum weight recorded was 99 pounds, while the maximum was 234 pounds. A 95% confidence interval for the population mean was estimated to be between 144 and 155 pounds, providing a range within which the true average weight is likely to fall with high confidence.

This data suggests that most individuals in the sample weigh around 149 pounds, with some variation, and there is high certainty that the overall population’s average weight lies within this narrow interval. The histogram visualization (Appendix A) supports the normal distribution assumption, reaffirming the use of mean and standard deviation for descriptive purposes.

Analysis of Age

The age data encompassed 100 subjects ranging from 18 to 74 years. An initial histogram indicated a significant skewness, with a concentration of younger ages and a tail extending toward older ages. Consequently, the data was identified as not normally distributed, necessitating the use of median and interquartile range (IQR) to describe central tendency and dispersion accurately.

The median age was 36 years, meaning half of the participants were younger than 36, and half were older. The interquartile range was approximately 20.5 years, with a middle 50% of the subjects falling within roughly ±10 years of the median. Since the data is skewed, a confidence interval for the mean is not readily applicable. The minimum age was 18, and the maximum was 74 years, reflecting a broad age distribution.

The skewed distribution suggests that the sample population is younger overall, with fewer elderly subjects, which is typical in many health-related studies. The histogram in Appendix A visually confirms the skewness, while the descriptive statistics in Appendix B support using median and IQR as more appropriate descriptors than mean and standard deviation.

Analysis of Education Level

Educational attainment was categorized into three levels: no high school diploma, high school diploma, and college or college graduate degree. The sample showed that 13% of subjects had no high school diploma, 44% had completed high school, and 43% held college or higher degrees. A bar chart (Appendix D) visually presents these proportions, illustrating the educational composition of the sample.

The majority of subjects had at least a high school diploma, with nearly half holding college qualifications. These proportions are indicative of a relatively educated sample, which can have implications for interpreting other health or demographic data collected alongside. The bar chart effectively communicates the distribution of education levels across the sample population.

Overall, these descriptive analyses provide comprehensive insights into the sample's characteristics, supporting further inferential statistical analyses or policy implications based on the demographic and health-related variables.

Conclusion

This descriptive statistics report demonstrates the importance of selecting appropriate measures based on data distribution. For normally distributed variables like body weight, mean and standard deviation offer precise summaries, while for skewed data such as age, median and IQR are more accurate descriptors. The visualization tools—histograms and bar charts—are crucial in assessing distribution and proportions, facilitating an intuitive understanding of the data. These descriptive insights form a foundation for subsequent analytic or research endeavors, ensuring accurate interpretation and decision-making.

References

• Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.
• Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: a guide for non-statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486-489.
• Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis: A global perspective. Pearson.
• Kirk, R. E. (2013). Experimental design: Procedures for the behavioral sciences. Sage.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson.
• Weiss, N. A. (2012). Introductory statistics. Addison-Wesley.
• Sheskin, D. J. (2004). Handbook of parametric and nonparametric statistical procedures. CRC press.
• Altman, D. G., & Bland, J. M. (1994). Diagnostic tests. 1: Sensitivity and specificity. BMJ, 308(6943), 1552.
• Ullman, J. B., & Bentler, P. M. (2013). Structural equation modeling. In Handbook of psychological assessment (pp. 527-549). Guilford Publications.
• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics, 5th Edition. Sage.