Which of the following best describes the difference between a $\mathrm{frequency} \mathrm{polygon}$ and an $\mathrm{ogive}$ in $\mathrm{frequency} \mathrm{distributions}$?

• A. A $\mathrm{frequency} \mathrm{polygon}$ uses bars to represent frequencies, while an $\mathrm{ogive}$ uses dots to represent individual data values.
• B. A $\mathrm{frequency} \mathrm{polygon}$ is used for qualitative data, while an $\mathrm{ogive}$ is used for quantitative data.
• C. A $\mathrm{frequency} \mathrm{polygon}$ displays the frequencies of class intervals using line segments connected at class midpoints, while an $\mathrm{ogive}$ displays cumulative frequencies using points plotted at upper class boundaries.
• D. A $\mathrm{frequency} \mathrm{polygon}$ shows cumulative relative frequencies, while an $\mathrm{ogive}$ shows only raw frequencies.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand what a frequency polygon is. A frequency polygon is a graphical representation of the distribution of a dataset. It is created by plotting points at the midpoints of each class interval on the x-axis and their corresponding frequencies on the y-axis, then connecting these points with straight line segments.
2. Step 2: Understand what an ogive is. An ogive is a graph that represents cumulative frequencies. It is constructed by plotting points at the upper class boundaries on the x-axis and the cumulative frequencies on the y-axis, then connecting these points with line segments.
3. Step 3: Compare the two graphs based on what they represent. A frequency polygon shows the frequency of each class interval individually, while an ogive shows the accumulation of frequencies up to a certain class boundary.
4. Step 4: Note the key differences in plotting. Frequency polygons use class midpoints for the x-axis values and plot frequencies, whereas ogives use upper class boundaries for the x-axis values and plot cumulative frequencies.
5. Step 5: Conclude that the correct description is that a frequency polygon displays frequencies of class intervals connected at class midpoints, and an ogive displays cumulative frequencies plotted at upper class boundaries.