Histograms, Frequency Polygons, and Time Series Graphs · Exercise 13

Often, cruise ships conduct all onboard transactions, with the exception of souvenirs, on a cashless basis. At the end of the cruise, guests pay one bill that covers all onboard transactions. Suppose that 60 single travelers and 70 couples were surveyed as to their onboard bills for a seven-day cruise from Los Angeles to the Mexican Riviera. Following is a summary of the bills for each group:

\begin{array}{|c|c|c|}\hline \text{Amount ($)} & \text{Frequency} & \text{Relative Frequency} \\ \hline \text{51–100} & \text{5} & \\ \hline \text{101–150} & \text{10} & \\ \hline \text{151–200} & \text{15} & \\ \hline \text{201–250} & \text{15} & \\ \hline \text{251–300} & \text{10} & \\ \hline \text{301–350} & \text{5} & \\ \hline\end{array}

\begin{array}{|c|c|c|}\hline \text{Amount ($)} & \text{Frequency} & \text{Relative Frequency} \\ \hline \text{100–150} & \text{5} & \\ \hline \text{201–250} & \text{5} & \\ \hline \text{251–300} & \text{5} & \\ \hline \text{301–350} & \text{5} & \\ \hline \text{351–400} & \text{10} & \\ \hline \text{401–450} & \text{10} & \\ \hline \text{451–500} & \text{10} & \\ \hline \text{501–550} & \text{10} & \\ \hline \text{551–600} & \text{5} & \\ \hline \text{601–650} & \text{5} & \\ \hline\end{array}

(a) Fill in the relative frequency for each group.
(b) Construct a histogram for the singles group. Scale the x-axis by $50 widths. Use relative frequency on the y-axis.
(c) Construct a histogram for the couples group. Scale the x-axis by $50 widths. Use relative frequency on the y-axis.
(d) Compare the two graphs:
(a) List two similarities between the graphs.
(b) List two differences between the graphs.
(c) Overall, are the graphs more similar or different?
(e) Construct a new graph for the couples by hand. Since each couple is paying for two individuals, instead of scaling the x-axis by $50, scale it by $100. Use relative frequency on the y-axis.
(f) Compare the graph for the singles with the new graph for the couples:
(a) List two similarities between the graphs.
(b) Overall, are the graphs more similar or different?
(g) How did scaling the couples graph differently change the way you compared it to the singles graph?
(h) Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person as a couple? Explain why in one or two complete sentences.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §2.2 Histograms, Frequency Polygons, and Time Series Graphs · Exercise 13