Final answer:
The numbers of touchdowns in a football game are considered quantitative discrete data, as they are counted and take specific numerical values. This type of data is essential for trends analysis and comparisons in various fields.
Step-by-step explanation:
The numbers of touchdowns in a football game would be considered as quantitative discrete data. This is because touchdowns are counted per game and can only take on certain numerical values such as 0, 1, 2, and so on. Thus, when a football league reports that the mean number of touchdowns per game was five and a study is done to determine if this mean has decreased, they are dealing with quantitative data.
Quantitative data refers to any data that can be quantified and is the result of counting or measuring attributes. Quantitative data is crucial in many fields, including science, business, and social studies, as it helps to understand trends and make comparisons. For instance, the number of touchdowns in various games across a season can reveal trends about offensive effectiveness or rule changes impacting scoring.
To discern if the mean number of touchdowns has decreased, one would statistically analyze the current touchdown data and compare it to the historical mean of five touchdowns per game using appropriate statistical tests like the t-test for mean comparison.