Instructions
In Module 2, we are learning about three primary measures of central tendency (mean, median, and mode) and three primary measures of dispersion (variance, standard deviation, and interquartile range).
Suppose over a 6-month period, you tracked the miles per gallon you logged in a vehicle you are driving. For example, if you drove 240 miles on 10 gallons of gas, the average miles per gallon would be 240/10=24 miles per gallon. One can expect the miles per gallon will change depending upon driving habits, the amount of time driving in the city versus highway driving, and the total weight of the vehicles.
Given this set of data you accumulated over 6 months, which measure of central tendency and which of dispersion do you think would best afford you an understanding of the distribution of this data? Be sure to explain why you selected each measure and why the one you selected may be better than the other choices.
Submission
Our discussions are a valuable opportunity to have thoughtful conversations regarding a specific topic. You are required to provide a comprehensive initial post with three to four well-developed paragraphs that include a topic sentence and at least three to five supporting sentences with additional details, explanations, and examples. The initial post is due by the due date listed on the syllabus Calendar of Activities. In addition, you are required to respond substantively to the initial posts of at least two other classmates on two different days. All posts should be reflective and well written, meaning free of grammar, sentence structure, and other mechanics errors.
Grading
This discussion is worth 25 points toward your final grade and will be graded using the Discussion Rubric. Please use the rubric as a guide toward successful completion of this discussion.
Reply to this student’s message below please
“In analyzing the distribution of the miles per gallon data tracked over a 6-month period, I believe that the mean and standard deviation would be the most appropriate measures of central tendency and dispersion.
Firstly, the mean would provide valuable insights into the average miles per gallon achieved during the 6-month period. By calculating the mean, we can obtain a measure of central tendency that takes into account all the individual data points, providing a representative value. This would allow us to understand the overall average fuel efficiency of the vehicle and make comparisons with other similar vehicles or industry standards. Considering that the miles per gallon may vary depending on driving habits, the mean would help identify any significant changes in fuel efficiency over time, allowing us to monitor the effectiveness of any driving habit modifications or vehicle maintenance.
Secondly, the standard deviation would be a suitable measure of dispersion to assess the spread of the miles per gallon data. Given that factors such as driving habits, city versus highway driving, and vehicle weight can influence fuel efficiency, the standard deviation would provide information about the degree of variability in the dataset. A higher standard deviation would indicate a wider range of miles per gallon values, reflecting the impact of these factors on the data. This information would be valuable in understanding the consistency or inconsistency of fuel efficiency and identifying sources of variation that may require further investigation, such as changes in driving patterns or vehicle conditions.
While the median and the interquartile range could also be considered, I believe the mean and standard deviation would offer a more comprehensive understanding of the distribution of the data. The median may not capture the full range of values and could potentially overlook extreme values that significantly impact fuel efficiency. Similarly, the interquartile range focuses only on the middle 50% of the data, potentially disregarding important outliers that may hold crucial information about fuel efficiency. By choosing the mean and standard deviation, we ensure that we consider the entire dataset and account for both the central tendency and dispersion, providing a more robust analysis of the miles per gallon data.”
