Question

Restaurant Bill by Sex Exercise 2.153 describes a study on the cost of meals when groups pay individually or split the bill. One of the variables in SplitBill also records the Sex of each subject. (a) Provide a numerical summary to compare costs of orders between females and males. (b) Create and comment on a graphical display to compare costs by \(\operatorname{Sex}\).

Short answer

The numerical summary will offer statistics—mean, median, standard deviation, min, and max—of the spending habits of both females and males. The graphical display (side-by-side box plots) will show a comparative visual representation of spendings by Sex, and any observations such as differences in dispersion, presence of outliers, and similar patterns should be highlighted.

Step-by-step solution

Organize the Data and Calculate Summary Statistics

A vital part of data analysis is organizing the data so that it's understood easily. Generate a table with segregated data of bills by Sex. Then, calculate key numerical statistics such as the mean, median, standard deviation, minimum and maximum costs for both males and females. This will give a brief numeric summary of the cost comparison between females and males.

Generate a Graphical Display

After organizing the data and deriving summary statistics, create a side-by-side box plot to compare the cost by Sex. Each individual box-and-whisker plot can represent the Male and Female groups, showing the median cost, spread (from Q1 to Q3), and any possible outliers. This graph aids in the visual comparison of costs by Sex, showcasing not only the central tendency of data, but also its spread.

Interpret the Results

Discuss the statistics: What do the numerical summaries tell us about the differences in cost of orders between the sexes? How does the distribution look on the box plots? Are there outliers? If so, which group has more? The interpretation of this information will lead to insights into the spending habits of men and women in restaurants.