MATH 225 Week 5 Assignment: Lab

MATH 225 Week 5 Assignment: Lab

Student Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Week 5 Lab Assignment

For this study, the heights of ten female friends were recorded to analyze basic statistical measures. The sample represents a biased, convenience sample because all participants were friends who verbally reported their heights rather than being physically measured. The heights collected were: 5’4” (64 inches), 5’4” (64 inches), 5’5” (65 inches), 5’5” (65 inches), 5’6” (66 inches), 5’6” (66 inches), 5’6” (66 inches), 5’7” (67 inches), 5’7” (67 inches), and 5’9” (69 inches).

Using Microsoft Excel, the mean height of the group was calculated to be 65.9 inches, with a sample standard deviation of 1.5239 inches. Additional statistical calculations showed a sample variance of 2.3222, a population variance of 2.0900, and a population standard deviation of 1.4457. These measures provide insight into the variability and distribution of the heights within this sample.

When comparing my height of 5’3” (63 inches) to the group mean, I am shorter than the average participant. The sampling method, a convenience sample, was selected primarily for ease of data collection via a group text message due to COVID-19 restrictions. This approach introduces inherent bias since participants were not randomly selected. The study was conducted in Sacramento, California, with participants aged 29 to 35 years. All participants were female, predominantly Caucasian, with two identifying as Hispanic. Interestingly, the two Hispanic participants were among the shortest in the group, yet I remained the shortest overall. Additionally, some participants reported their heights with uncertainty (e.g., “I think I’m around 5’6””), which further introduces potential bias.

The distribution of heights was further analyzed using the Empirical Rule, which states that approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations (Glen, 2020). For this dataset, 68% of participants were between 64.4 and 67.4 inches tall, 95% were between 62.9 and 68.9 inches, and 99.7% fell between 61.3 and 70.5 inches. With my height being 63 inches, I fall in the lower 2.84% of the population, indicating that 97.15% of the group is taller than I am. This analysis demonstrates how individual measurements relate to the overall distribution of the sample.

Row and Columns Table

Empirical Rule Distribution

References

Glen, S. (2020, September 20). Empirical Rule (68-95-99.7) & Empirical Research. Retrieved October 02, 2020, from https://www.statisticshowto.com/empirical-rule-2/

MATH 225 Week 5 Assignment: Lab

Holmes, A., Illowsky, B., & Dean, S. (2019). Introductory Business Statistics (4.0). Retrieved from https://openstax.org/details/books/introductory-business-statistics