Question

Seven of the ten largest cities in the world are in the Eastern Hemisphere (including the largest: Tokyo, Japan) and three are in the Western Hemisphere. \(^{11}\) Table 1.4 shows the populations, in millions of people, for these cities. (a) How many cases are there in this dataset? How many variables are there and what are they? Is each categorical or quantitative? (b) Display the information in Table 1.4 as a dataset with cases as rows and variables as columns. $$ \begin{array}{ll} \hline \text { Eastern hemisphere: } & 37,26,23,22,21,21,21 \\ \text { Western hemisphere: } & 21,20,19 \\ \hline \end{array} $$

Short answer

There are 10 cases (cities) in the dataset. The variables are Hemisphere (categorical) and Population (quantitative). The data, when reorganized into a dataset with cases as rows and variables as columns, assigns each city to a specific Hemisphere and provides a Population value (in millions) for each case.

Step-by-step solution

Identify Cases and Variables

Looking at the dataset, the number of 'cases' can be identified as each individual city. Given that there are ten cities mentioned (seven from Eastern Hemisphere and three from Western Hemisphere), there are ten cases in this dataset. The variables in the dataset are 'Hemisphere' and 'Population.' The 'Hemisphere' variable is categorical as it groups the cities into two distinct categories: Eastern and Western hemispheres. The 'Population' variable is quantitative as it provides a numerical value depicting the number of people (in millions) who reside within each city.

Reformat Dataset

To display the information in the given table 1.4 as a dataset with cases as rows and variables as columns, assign each city to a row and the related variables (Hemisphere and Population) to columns. It should be noted that the exercise does not provide the specific names for all of the cities, and thus they cannot be individually listed. However, the reformation can be generally understood like so: \[ \begin{tabular}{|c|c|c|} \hline \text{City} & \text{Hemisphere} & \text{Population} \\ \hline \text{City 1} & \text{Eastern} & \text{37} \\ \text{City 2} & \text{Eastern} & \text{26} \\ \vdots & \vdots & \vdots \\ \text{City 10} & \text{Western} & \text{19} \\ \hline \end{tabular}\]

Summary of Dataset

In this dataset the cases are individual cities and the variables are 'Hemisphere' (categorical) and 'Population' (quantitative). There are 10 cities in total, with 7 in the Eastern Hemisphere and 3 in the Western Hemisphere. The populations of these cities, listed in millions, ranges from 19 to 37.