Final answer:
To analyze the frequency and patterns of ski injuries, the most suitable data analysis type is histogram construction. It provides a clear visual representation of injury occurrences, unlike other methods that either focus on trends over time or associations between categorical variables.
Step-by-step explanation:
To understand the frequency and patterns of injuries treated during the ski season at a hospital near a ski resort, the most appropriate type of data analysis would be D. Histogram construction. A histogram is a graphical representation that organizes a group of data points into specified ranges, which would effectively showcase the distribution and frequency of different types of ski injuries. This would allow observers to quickly assess the most common injuries and their occurrence rate.
Options A (Linear regression) and C (Time-series analysis) could provide insights into trends over time or correlation between two variables, but they do not directly address frequency and patterns of categories of data. B (Chi-square analysis) is used to determine if there is a significant association between categorical variables, which isn't the primary goal here.
It is also important to note that the number of times per week members use a health club is quantitative discrete data since it deals with counts that can only take on specific values within a range. The sampling method used by the student who selected every eighth house around a park would be considered systematic sampling.
In terms of injuries at the ski resort and quantifying things like mean age for ski lessons, mean recovery period, or mean health costs for insurance purposes, these would involve the use of descriptive statistics to summarize and describe features of a dataset.
Therefore answer is D. Histogram construction.