Mathematics
Mathematics
Problem
Answer the following sub-questions related to grouped data with unequal class intervals. a. (a) Define frequency density in the context of a grouped frequency distribution. b. (b) Give one clear reason why, when drawing a histogram for classes of different widths, the vertical axis is marked with frequency densities instead of raw frequencies.Intuitive explanation
When data is grouped into classes of different widths, you can't just compare raw frequencies—you need to account for how spread out each class is. The key insight is to use frequency density (frequency ÷ class width) to normalize each class, making it fair to compare how densely packed the data really is in each interval. This unlocks everything: finding the mode, drawing histograms correctly, and estimating statistics like the median.
Intuitive explanation
When data is grouped into classes of different widths, you can't just compare raw frequencies—you need to account for how spread out each class is. The key insight is to use frequency density (frequency ÷ class width) to normalize each class, making it fair to compare how densely packed the data really is in each interval. This unlocks everything: finding the mode, drawing histograms correctly, and estimating statistics like the median.