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-Suppose you are comparing frequency data for two different groups, 25 managers and 150 blue collar workers. Why would a relative frequency distribution be better than a frequency distribution?

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The Answer is When comparing frequency data for two different groups of different sizes, such as 25 managers and 150 blue collar workers, a relative frequency distribution is often more informative than a simple frequency distribution. This is because a relative frequency distribution takes into account the size of the group when presenting the data, which allows for a more accurate comparison between groups of different sizes.

A frequency distribution simply counts the number of occurrences of each value or category within the data set. For example, if you were looking at the frequency of certain decisions made by managers versus blue collar workers, the frequency distribution would show the raw counts. However, because the group of blue collar workers is much larger (150) than the group of managers (25), the raw counts would likely be higher for the blue collar workers simply due to their greater number, not necessarily because their behavior or choices are inherently different.

On the other hand, a relative frequency distribution calculates the proportion or percentage of the total that each category represents. This is done by dividing the frequency of each category by the total number of observations in the group. By using relative frequencies, you can compare the behavior or choices of the two groups on a more equal footing, as each group's data is scaled according to its size.

For example, if 10 out of 25 managers (40%) made a certain decision, and 60 out of 150 blue collar workers (40%) made the same decision, the relative frequency distribution would show that the proportion is the same across both groups, despite the raw frequency being different. This allows for a fair comparison and can provide insights that might be overlooked if only raw frequencies were considered.

In summary, a relative frequency distribution is better than a frequency distribution for comparing groups of different sizes because it normalizes the data, allowing for a direct comparison of the proportions or percentages across the groups, which is a more accurate reflection of the underlying patterns or trends.

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