For grouped interval data, which graphs are appropriate to display the distribution?

For grouped interval data, which graphs are appropriate to display the distribution?

• A. Bar Graph
• B. Histogram
• C. Polygon
• D. Either Histogram or Polygon

Answer: (D)

When data are grouped into regular intervals, you want a display that reflects the continuous nature of the variable across those intervals. A histogram does this by drawing adjacent rectangles for each class, with widths equal to the class width and heights representing the frequencies (or relative frequencies); the bars touch to show continuity between neighboring intervals. A frequency polygon provides a similar view: plot a point at the class midpoint on the horizontal axis with the corresponding frequency on the vertical axis, and connect the points with straight lines. This shape makes it easy to see the overall distribution, its skew, and whether there are multiple modes. The bar graph is less appropriate for grouped interval data because it treats each interval as a separate, discrete category with gaps between bars, which can obscure the idea of a continuous distribution across the intervals. So, for grouped interval data, either a histogram or a frequency (polygon) is the best choice to display the distribution.

When data are grouped into regular intervals, you want a display that reflects the continuous nature of the variable across those intervals. A histogram does this by drawing adjacent rectangles for each class, with widths equal to the class width and heights representing the frequencies (or relative frequencies); the bars touch to show continuity between neighboring intervals. A frequency polygon provides a similar view: plot a point at the class midpoint on the horizontal axis with the corresponding frequency on the vertical axis, and connect the points with straight lines. This shape makes it easy to see the overall distribution, its skew, and whether there are multiple modes.

The bar graph is less appropriate for grouped interval data because it treats each interval as a separate, discrete category with gaps between bars, which can obscure the idea of a continuous distribution across the intervals.

So, for grouped interval data, either a histogram or a frequency (polygon) is the best choice to display the distribution.