Greek tragedies

of the many Greek tragedies that are thought to have existed around the 5th century BCE, it seems that complete texts are rare

only those from Aeschylus, Sophocles and Euripides are extant

the boxplot shows the word lengths from the written tragedies of these three writers

comment on the differences

boxplots of heights

comparing heights of girls and boys

what comments can be made from this boxplot? 

comparing two data sets

the longevity of US Presidents has interesting features

a powerpoint is here

many students will sensibly think that more recent Presidents lived to an older age on average  due to advances in health care, nutrition and other factors that have led to a (general) increase in life expectancy

some Presidents in this data set are not counted (but could be)
this is to keep the sizes of the data sets the same (with apologies) for a frequency graph comparison

the data sets


















a possible question to direct the study:

the analysis could use some of the following techniques
which are overlapping in terms of what they tell you:

little point in estimating the means - just to practise this technique

cumulative graph matching

match the cumulative frequency graph to the associated boxplot

boxplot data set sizes

there are complications involved in sorting out where the 1st and 3rd quartiles lie for fairly small data sets
most sources simplify matters...
and anyway, for discrete distributions, there is no convention for selecting the quartile values

when choosing a size for a data set it is easiest to have a total of the form 4n + 3 with all the quartiles being actual numbers in the data set (ignore the median value to locate the remaining quartiles...)

a data set size of the form 4n + 2 has the median between the middle two numbers and then (for simplicity) the other quartiles are in the data set

for a size 4n + 1 data set, the 1st and 3rd quartiles are half-way between numbers and the median is in the data set

for a size 4n data set, all of the quartiles are half-way between data set values

this covers all possible data set sizes

for smallish data set sizes I usually suggest that students draw a set of tick marks so that they can see where the quartiles are located

however, these are simplifications
there are some rules that make sense but seem to complicate matters

for real data analysis, people do not deal with such small data set sizes...