Chapter 1 Introduction to statistics
Exercise 1.1 Try to characterize the following variables in terms of the types numerical and continuous, numerical and discrete, categorical and ordinal, categorical and nominal.
- The classification of a company in a stock market as belonging to industry, mining, energy, telecom, transport, etc…
- The monthly fuel cost for a transport company.
- The main mode of transportation a person used traveling to work on a given day: car, bus, bike, walk, taxi, subway, passenger in private car, other.
- The number of transportation modes a person used traveling to work on a given day (For instance, it is 2 if a person went by subway and taxi).
- A stock market analysts recommendation for particular stocks as Sell, Hold, Buy, Strong buy.
- The share price of Apple on the New York Stock exchange at a given time.
Exercise 1.2 In a sample of \(n = 200\) medical operations at a hospital, the average duration was \(\bar{x} = 56\) minutes, with a standard deviation of \(S = 11\) minutes. Supposing the distribution of times is fairly symmetrical, find an interval that is likely to include about 95% of the durations of such operations. Discuss how such information can be used for planning purposes at the hospital.
Exercise 1.3 Take a look at the scatterplot in figure 1.1. This shows the urbanization percentage vs the female life expectancy in the sample data world95
. Consider some country not in the sample.
Suppose you knew that the female life expectancy was about 50 in the country. What would you guess for the urbanization % in the country? Give an approximate interval where you would expect to find the number.
Repeat for a country not in the sample, with female life expectancy at 80 years.
Do the data and the strong correlation indicate that it is more healthy to live in a city than on the countryside?