Question 1 Of 2050 Points A Student Was Interested In The CI

Question 1 Of 2050 Pointsa Student Was Interested In The Cigarette Sm

A student was interested in the cigarette smoking habits of college students and collected data from an unbiased random sample of students. The data is summarized in the following table: Males Surveyed 50 Females Surveyed 75 Males Who Smoke 20 Females Who Smoke 25 Males Who Do Not Smoke 30 Females Who Do Not Smoke 50. Why is the table NOT a frequency distribution? A. The number of males does not equal the sum of males that smoke and do not smoke. B. The classes are not mutually exclusive. C. There are too many classes. D. Class limits cannot be computed.

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The primary focus of this analysis is to understand why the provided data table does not qualify as a frequency distribution. To understand this, it is essential to first clarify what constitutes a frequency distribution. A frequency distribution is a summary table that displays the frequency, or number of occurrences, of each class or category in a data set. Typically, it organizes data into mutually exclusive classes or categories, ensuring each data point falls into only one category, and the total frequencies sum up to the total number of observations.

In the given table, the data summarizes the number of college students surveyed, divided into categories based on smoking habits, with separate counts for males and females. The counts are as follows: 50 males surveyed, with 20 smokers and 30 non-smokers; 75 females surveyed, with 25 smokers and 50 non-smokers. Although the table presents counts across categories, it lacks the structure characteristic of a frequency distribution in several ways.

One key reason why the table is not a frequency distribution is the issue of mutually exclusive classes. For a table to qualify as a frequency distribution, each observation must belong exclusively to one category—there should be no overlap or ambiguity. In the context of this data, the categories are clearly defined as 'smoke' or 'do not smoke,' which are mutually exclusive and collectively exhaustive, assuming the total counts are correct and mutually exclusive. However, the question hints at some underlying issues, such as the totals not aligning, which suggests some inconsistency or misclassification.

Another possible interpretation is that the table mixes counts of individuals without explicitly tabulating their distribution in a way that fits standard frequency distribution practices. A typical frequency distribution table would include class intervals and corresponding frequencies, or categories with clear, non-overlapping definitions. The provided table, being a simple tally of counts in different categories, does not display the hierarchical organization or the class limits characteristic of a frequency distribution.

Looking at the options provided in the question, option A states: "The number of males does not equal the sum of males that smoke and do not smoke." This indicates an inconsistency in the total counts, which can make the table invalid as a frequency distribution. Option B suggests that classes are not mutually exclusive, which violates one of the fundamental principles of a frequency distribution if categories overlap. Option C mentions too many classes, which is less relevant, and option D, class limits cannot be computed, which is not necessarily applicable here since class limits pertain to grouped continuous data.

Therefore, the primary reason the data table is not a frequency distribution appears to be the absence of mutually exclusive, well-defined classes with clear class limits or intervals, and potential inconsistencies in the counts' totals. Thus, the most precise answer aligns with option B, that the classes are not mutually exclusive, or more broadly, the data does not conform to standard frequency distribution structure.

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