## 3 Characterizing Public Transportation System
### Results and Discussion
#### 3.3.1. Cardholders  
The sales dataset holds transactions made with 654,228 different smart cards. As explained in Section 3.2.1, several passengers may travel together using a single smart card. However, the vast majority of passengers use their own personal smart card: over 97% of transactions correspond to individual tickets. Therefore, smart cards can be confidently assumed to represent a single passenger. This is a key assumption used in the OD matrix estimation presented in Section 4, where all passengers under the same smart card are assumed to travel from origin to destination together. Thus, the fact that few group trips are performed using the same smart card provides a certain level of robustness to the OD matrix estimation model.  
Data analysis can also give insight into the frequency of use of the transportation system. Table 1 reports descriptive statistics of daily and monthly transactions per smart card, including the minimum (min) and maximum (max) values, the 25 th (Q1), 50 th (Q2), and 75 th (Q3) percentiles, and the Median Absolute Deviation (MAD). The 50 th percentile corresponds to the median of the distribution of transactions per smart card. Monthly statistics consider all transactions done by each cardholder. Daily statistics only consider days for which at least one transaction was made. Values corresponding to the complete dataset are presented (all weekdays) and also considering only working days and only weekends. Additionally, daily and monthly sales distributions considering all weekdays are displayed in Figures 5 and 6, respectively. Plots are limited to the most occurring values for better visualization.  
Regarding monthly use, the median cardholder performs 22 transactions per month, nearly one transaction per working day in the month. However, the MAD is 22.5, suggesting a significant difference between regular and sporadic users of the public transportation system. Regarding daily use, the median cardholder performs two smart card transactions each active day (i.e., each day with at least one transaction). Additionally, more cardholders perform four rather than three transactions (see Figure 5), which could be explained by passengers using trips involving a transfer. Thus, two transactions correspond to the outward trip and the remaining two transactions to the return trip. Daily usage is higher on working days than weekends when looking at the top quartiles. Additionally, monthly usage is also sensibly higher on working days than on weekends. Taking into account that the studied month had nine days in weekends, users perform (in median) roughly one transaction in the whole weekend vs. one transaction per day on working days. This is consistent with the information from the 2016 mobility survey, which states that commutes to work are the main purpose of traveling, accounting for nearly 30.9% of all trips. An in-depth analysis of the effect of the public transportation system in employment in Montevideo is studied in [21].  
Identifying outliers within the smart card use statistics can be a useful tool for authorities of the public transportation system. On the one hand, cardholders with very few monthly transactions can be identified by their card ID. In the studied dataset, 15,440 cardholders performed a single trip during the whole month of May 2015. Targeted marketing campaigns could be designed to encourage disengaged citizens to use public transportation more frequently. On the other hand, cardholders with a large number of transactions can also be identified. In the studied dataset a single card was found to perform 54 transactions in a single day. This information can help authorities to further investigate and identify possible abuses to the system.