Final answer:
The question revolves around creating two-way frequency tables for a set of numbers and their multiples, calculating percentages of surveyed data, and analyzing frequencies from experimental outcomes in Mathematics.
Step-by-step explanation:
The subject of the question is Mathematics, specifically dealing with the topics of probability, frequency, and data representation in the form of Venn diagrams, two-way frequency tables, and histograms. High school students often encounter these concepts in their coursework.
Two-Way Frequency Tables
To complete a two-way frequency table based on the teacher's set of 16 numbers, one must tabulate the number of numbers that are multiples of 3, multiples of 4, both, and neither. This process involves examining each number, determining its factors, and placing it in the appropriate category relative to multiples of 3 and 4.
Frequency and Probability
When conducting a survey or poll, such as counting the number of siblings students have or the number of classes they are taking, it is essential to organize the data into frequency tables. To calculate percentages, like the percentage of students with no siblings or the probability of a student being in a club, you use the frequencies to form ratios, then convert these to percentages or probabilities.
Frequencies in Experiments
When conducting experiments, such as rolling a die, keeping track of frequencies helps to determine the likelihood of certain outcomes. This can further be analyzed using tables and graphs, which offer a visual representation of data and make it easier to conclude.