Statistics - Creating a data set from a summary table

[4quila]

Homework Statement

In his paper "regression towards mediocrity in hereditary stature" Francis Galton collects data on stature of children (928 obs.) & parents (205 obs.) now as part of my project i have been asked to recreate the original data set. However taking children the data set runs from 64.5,65.5,...,72.5 inches with corresponding numbers of obs. Fair enough. However we have 14 observations labelled "below" and 4 labelled "above" and the problem statement is;

"For objects labelled above or below you must assume some particular values. Please state these explicitly in a table and justify with one sentence."

Homework Equations

The Attempt at a Solution

Clearly if any of these above or below terms are large outliers they will have an impact on the regression so i want to avoid that. But i am struggling to think of a value for these variables to take? Do i assign them values so as to ensure the mean for example is unaffected? Or give them values so they form a nice looking histogram?

I guess in short i am asking if there is a common practice for this kind of thing? Or if it is just an arbritary assignment as long as i can justify it plausibly?

All help much appreciated.

 

[mighty2000]

I understand your concern about outliers and the impact they may have on regression. In this case, it is important to consider the purpose of the data collection and the analysis. If the outliers are large and have a significant impact on the regression, it may be necessary to remove them from the dataset or address them separately.

However, for the purpose of recreating the original data set, it is important to follow the instructions and assign values to the "above" and "below" observations. One approach could be to assign them the average value of the observations in the dataset, or the median value if there are any extreme outliers. This way, the overall mean and median of the dataset will not be significantly affected.

Another approach could be to assign values based on the distribution of the rest of the data. For example, if the data follows a normal distribution, you could assign the "above" and "below" observations based on the mean and standard deviation of the rest of the data.

Ultimately, the specific values chosen for the "above" and "below" observations may be somewhat arbitrary, but it is important to justify them based on the purpose of the data collection and the analysis. I hope this helps and good luck with your project.