Measure of Central Tendency: Mean, Variance, and Standard Deviation

The small dataset pictured below (n=30) is adapted from MEPS and could be used to explore the relationship among individuals’ self-reported health status, their insurance coverage, and their work intensity (measured in hours per week). The data are also uploaded onto Canvas in Excel and Stata formats. You may calculate answers to these questions in any way that you wish.
a. Write a brief paragraph (emphasis on brief) suitable for publishing that summarizes the data for readers. Provide an appropriate measure of central tendency for each of the four variables (no need to discuss idnum since it’s not truly a variable). Use some of the good writing practices from the Miller book, such as varied, non-repetitive sentence structures and appropriate levels of detail. There is no need to include any measures of dispersion. Assume your audience is made up of generally smart people who have taken quant classes like this, but they don’t know anything about the specific topic.
b. Calculate the mean number of hours worked for each of the five health categories. Very briefly describe the relationship you see and provide a plausible explanation.
c. What are the variance and standard deviation of weekly hours?
d. Using MBB’s definition (page 78), how many observations are considered outliers for their weekly work hours? Report the id number for each and the number of standard deviations away from the mean they fall.
e. Create z-scores for each individual in the dataset. (If you do this in Excel, I’d recommend adding new columns to the right of the current variables and gradually filling them in with each step necessary to create a z-score. If you do this in Stata, you can first use the summarize command to get the statistics you need, then the generate command to create a variable called z.)
Calculate the mean and standard deviation of the z scores and report both in decimal format (that is, do not report them using scientific notation or e notation we sometimes use for very large or small numbers).
How far off are the mean and standard deviation of the z-score from your expectations? Explain.
f. Suppose the survey administrator made a careless mistake while analyzing the dataset. She accidentally duplicated each of the 30 observations to make a new dataset of n=60 with each observation represented twice. (Honestly, I’ve made far graver mistakes than this.)
Would the variance get bigger, smaller, or stay the same? Explain.
Show your math on these:
g. Using the information at hand, what number of work hours would lie 1.5 standard deviations below the mean?
h. Hypothetically, how big would the standard deviation have to be in order for a 10-hour work week to fall 2 standard deviations below the mean?
i. Finally, who works more in relative terms compared to other members of their sex (that is, who represents a greater deviation from their sex’s mean): A man who works 60 hours or a woman who works 50 hours?