Write the advantages of a frequency polygon over a histogram.
The correct answer and explanation is:
A frequency polygon offers several advantages over a histogram when representing data. First, it provides a clearer visual comparison of different data sets. When comparing multiple sets of data, frequency polygons can be overlaid on the same graph, allowing for direct visual comparison. This is particularly useful when one needs to compare the distributions of different groups. In contrast, histograms often require separate graphs or use of different colors, which can make direct comparison more difficult.
Second, frequency polygons can present a smoother curve that highlights the overall shape of the distribution. This smoothness allows for easier identification of trends and patterns in the data, such as whether it is skewed, bimodal, or has a normal distribution. On the other hand, histograms, while useful for showing frequency, may present jagged or uneven bars, making it harder to see the underlying distribution without additional analysis.
Another advantage of frequency polygons is that they provide a better representation of continuous data. Histograms are typically used for discrete data or grouped data and may introduce arbitrary divisions that affect how the data is interpreted. A frequency polygon, however, is drawn by connecting the midpoints of class intervals, making it more suitable for showing trends in continuous variables.
Additionally, frequency polygons are more compact in presentation. When showing data in a single graph, frequency polygons can display several datasets without crowding or confusion, whereas histograms with multiple data sets can become overcrowded, making it harder to distinguish between them.
Lastly, frequency polygons are more flexible when it comes to the inclusion of cumulative data. They allow for easy plotting of cumulative frequencies, which is not as straightforward with histograms. This ability can provide deeper insights into data progression over intervals.