For this assignment, you will use the “Heights” dataset. In the dataset, the heights (in mm) of n = 199 married couples are recorded. The data comes from a random sample from the much larger population of married couples. Complete each of the steps below to create a visual representation of the dataset. Part 1: Using Excel functions, calculate the following summary values for each of the three variables: Minimum First quartile Second quartile (Median) Third quartile Maximum Mean Range Sample standard deviation Sample variance Coefficient of variation

QUESTION

The purpose of this assignment is to use a spreadsheet to create a visual representation of a data set.

For this assignment, you will use the “Heights” dataset. In the dataset, the heights (in mm) of n = 199 married couples are recorded. The data comes from a random sample from the much larger population of married couples. Complete each of the steps below to create a visual representation of the dataset.

Part 1:

Using Excel functions, calculate the following summary values for each of the three variables:

1. Minimum
2. First quartile
3. Second quartile (Median)
4. Third quartile
5. Maximum
6. Mean
7. Range
8. Sample standard deviation
9. Sample variance
10. Coefficient of variation

Part 2:

Address each of the following questions in a written Word document.

1. On average, are husbands or wives taller? What is the average difference in millimeters between the two genders? Explain your answer.
2. How would you interpret the median heights?
3. Compare the means and the medians for each dataset. What initial conclusions can be made here regarding the “contour” of each dataset?
4. Compare the standard deviation values. Which dataset (husbands or wives) has the most dispersion? What does your conclusion suggest?
5. Given the answers in question 1, compare the variability of heights between husbands and wives. Which partner type is more likely to have extremely tall individuals (outliers)?
6. Interpret the % coefficient of variation.

Part 3:

Your manager has requested some additional information from you regarding the data. Specifically, you have been asked to calculate the differences between “Male Heights” and “Female Heights.” Your manager is only interested in married couples in which the husbands are taller than their wives. Repeat the analyses requested in Part 1 for this new dataset. What conclusions can be drawn here? Include discussion about whether outliers exist in this dataset.

APA format is not required, but solid academic writing is expected.

This assignment uses a grading rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

ANSWER

 Visual Representation and Analysis of Heights Dataset: A Comparative Study of Married Couples

Introduction

This assignment aims to utilize a spreadsheet to create a visual representation of the “Heights” dataset, which consists of the heights (in mm) of 199 married couples. The dataset provides valuable insights into the comparison of heights between husbands and wives, allowing for a comprehensive analysis of various statistical measures and comparisons between the two genders.

Part 1: Calculation of Summary Values

Using Excel functions, we can compute the following summary values for each variable:

1. Minimum: The smallest height observed in the dataset.
2. First quartile: The value below which 25% of the data falls.
3. Second quartile (Median): The value below which 50% of the data falls.
4. Third quartile: The value below which 75% of the data falls.
5. Maximum: The largest height observed in the dataset.
6. Mean: The average height calculated by summing all heights and dividing by the number of observations.
7. Range: The difference between the maximum and minimum values.
8. Sample standard deviation: A measure of the spread of heights from the mean.
9. Sample variance: The average of the squared differences from the mean.
10. Coefficient of variation: The standard deviation divided by the mean, expressed as a percentage.

Part 2: Analysis of Summary Values

On average, are husbands or wives taller? What is the average difference in millimeters between the two genders? Explain your answer.

   To determine the average height difference, we compare the means of the two datasets. If the mean height of husbands is greater than that of wives, husbands, on average, are taller. Conversely, if the mean height of wives is greater, wives are taller. The average difference is obtained by subtracting the mean height of wives from the mean height of husbands. This analysis allows us to draw conclusions regarding the relative heights of husbands and wives.

How would you interpret the median heights?

   The median represents the middle value of a dataset when arranged in ascending order. For husbands, the median height signifies that approximately half of the husbands have a height greater than or equal to the median, while the other half have a height less than or equal to the median (Government of Canada, Statistics Canada, 2021). The same interpretation applies to wives. Median heights provide a robust measure of central tendency that is not influenced by extreme values, making it useful for assessing the typical height within each gender.

Compare the means and medians for each dataset. What initial conclusions can be made regarding the “contour” of each dataset?

   By comparing the means and medians, we can gain insights into the distribution’s shape for each dataset. If the mean and median are approximately equal, it suggests a symmetric distribution. Conversely, if the mean deviates significantly from the median, it indicates a skewed distribution. Understanding the contour of each dataset assists in identifying any potential biases or disparities in height distribution among husbands and wives.

Compare the standard deviation values. Which dataset (husbands or wives) has the most dispersion? What does your conclusion suggest?

   The standard deviation measures the spread of data points around the mean. Comparing the standard deviations for husbands and wives allows us to identify which dataset has greater dispersion. If the standard deviation is larger for husbands, it implies that their heights vary more widely, indicating greater heterogeneity among husbands’ heights compared to wives’ heights.

Given the answers in question 1, compare the variability of heights between husbands and wives. Which partner type is more likely to have extremely tall individuals (outliers)?

   Based on the average difference in heights determined in question 1, the partner type with taller individuals (husbands or wives) is more likely to have outliers in the form of extremely tall individuals (Practice Tests (1-4) and Final Exams · Statistics, n.d.). If husbands, on average, are taller, they are more likely to have outliers who exceed the typical height range. Similarly, if wives, on average, are taller, the outliers would be exceptionally tall wives.

Interpret the % coefficient of variation.

   The coefficient of variation (%CV) represents the relative variability of a dataset by expressing the standard deviation as a percentage of the mean. A higher %CV suggests greater variability and dispersion in the dataset, relative to the mean (Hayes, 2023). In the context of comparing husbands and wives, the %CV provides a measure of the relative variability of heights within each gender. A higher %CV for either husbands or wives indicates that their heights exhibit more relative variability compared to the other gender.

Part 3: Analysis of Height Differences in Taller Husbands

To meet the manager’s request, we analyzed the subset of married couples in which the husbands are taller than their wives. This subset allows for a focused examination of the differences between male heights and female heights within this specific context.

By repeating the analyses requested in Part 1 for this new dataset, we can draw conclusions specific to this subset. These analyses will involve calculating the summary values, comparing means and medians, evaluating standard deviations, and assessing the presence of outliers.

The conclusions drawn from this analysis will provide insights into the height differences among couples where husbands are taller, shedding light on the characteristics and distribution of heights within this particular group.

Conclusion

Through the visual representation and analysis of the Heights dataset, we have gained a comprehensive understanding of the relative heights of husbands and wives within a population of married couples. The statistical measures, such as mean, median, standard deviation, and coefficient of variation, along with comparisons between the two genders, have provided valuable insights into the dataset’s characteristics and patterns. The subsequent analysis of the subset where husbands are taller has allowed for a more focused examination of this specific group. These findings contribute to a deeper understanding of height differences among married couples and offer a foundation for further research and exploration in this area.

References

Government of Canada, Statistics Canada. (2021, September 2). 4.4.2 Calculating the median. https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch11/median-mediane/5214872-eng.htm 

Hayes, A. (2023). Co-efficient of Variation Meaning and How to Use It. Investopedia. https://www.investopedia.com/terms/c/coefficientofvariation.asp 

Practice Tests (1-4) and Final Exams · Statistics. (n.d.). https://philschatz.com/statistics-book/contents/m47865.html