1. You work for a company that manufactures lifts and you need to estimate the expected weight it needs to carry.  You know that the weights of passengers using the lift would vary both individually and as groups. Your job is to design a lift that would be able to carry 99% of all possible groups entering the lift at the same time. For the purpose of this exercise, you do not need to worry about the groups whose cumulative weight is in the heaviest 1%.  

Your company manufactures two versions of the lift: one small model with just enough space for five people and one large model with space for ten people. Answer the questions below:  

1.1 Search online for a dataset with people’s weights. Describe it and report where you found it (e.g., link to the website). Create diagrams showing the distribution of the weights in the dataset, using density curves, boxplots, violin chart etc. Add appropriate descriptive statistics (mean, median, standard deviation, range etc). Assume that this dataset is a representative sample of the passengers that would use your lift.

1.2 Sample your dataset, generating groups of five (for the small lift) and groups of ten (for the larger lift). Provide diagrams of the distribution of the expected weights for each of the two lifts, as well as the appropriate descriptive statistics. How do the distributions of the two lifts compare? How do they compare to the distribution of people’s weights?

1.3 Find the average weight of a person in the heaviest group that your design would support. You will need one measure for each type of lift. Can you explain the difference between the two measures?