For data measured on an ordinal scale (not necessarily interval), which graph is appropriate?

For data measured on an ordinal scale (not necessarily interval), which graph is appropriate?

• A. Bar graph
• B. Histogram
• C. Polygon
• D. Either histogram or polygon

Answer: (A)

For data measured on an ordinal scale, the key idea is that categories are ordered, but the distances between adjacent categories are not assumed to be equal. A bar graph fits this well because each category is shown as a separate bar, and its height reflects the frequency or proportion in that category. The gaps between the bars emphasize that the categories are distinct and not points on a continuous scale, which keeps the ordinal nature intact without implying equal intervals. A histogram, on the other hand, relies on numeric, continuous data and uses touching bars to suggest a smooth distribution with meaningful distances between values. Applying that to ordinal categories would falsely imply equal spacing between ranks. A frequency polygon (the line-graph version of a histogram) carries the same assumption of an underlying continuous variable, so it’s not appropriate for purely ordinal data. Therefore, the bar graph is the appropriate choice.

For data measured on an ordinal scale, the key idea is that categories are ordered, but the distances between adjacent categories are not assumed to be equal. A bar graph fits this well because each category is shown as a separate bar, and its height reflects the frequency or proportion in that category. The gaps between the bars emphasize that the categories are distinct and not points on a continuous scale, which keeps the ordinal nature intact without implying equal intervals.

A histogram, on the other hand, relies on numeric, continuous data and uses touching bars to suggest a smooth distribution with meaningful distances between values. Applying that to ordinal categories would falsely imply equal spacing between ranks. A frequency polygon (the line-graph version of a histogram) carries the same assumption of an underlying continuous variable, so it’s not appropriate for purely ordinal data. Therefore, the bar graph is the appropriate choice.