Suppose you have a dataset of exam scores grouped into intervals of 10 points ($0-10$, $10-20$, ..., $90-100$). If you create a histogram using frequency on the y-axis, which of the following histograms would represent the same data as one using relative frequency on the y-axis?

• A. A histogram with different bar heights but the same x-axis intervals
• B. A histogram with the bars rearranged in order of height
• C. A histogram with the y-axis showing cumulative frequency
• D. A histogram with the same shape but the y-axis labeled as proportion instead of count

Answer: (D)

Verified step by step guidance

1. Understand that a histogram represents the distribution of data by grouping values into intervals (bins) along the x-axis and showing the frequency (count) of data points in each bin on the y-axis.
2. Recognize that relative frequency is the frequency of each bin divided by the total number of data points, which converts counts into proportions or percentages.
3. Note that changing from frequency to relative frequency on the y-axis scales the heights of the bars by the same constant factor (the total number of observations), so the shape of the histogram remains the same.
4. Identify that rearranging bars or changing the y-axis to cumulative frequency alters the shape or interpretation of the histogram, so these do not represent the same data distribution as the original frequency histogram.
5. Conclude that the histogram with the same shape but the y-axis labeled as proportion (relative frequency) correctly represents the same data as the frequency histogram, just scaled differently.