Distinguish between frequency polygon and frequency curve.

A frequency polygon and a frequency curve are both graphical representations of frequency distributions, but they differ in terms of their construction and appearance.

Frequency Polygon:
A frequency polygon is a line graph that represents the data points by connecting the midpoints of the upper sides of the rectangles or bars in a histogram. It is constructed by plotting the frequency of each class or interval on the y-axis and the midpoint of each class on the x-axis. The points are then connected by straight lines, forming a polygon. The frequency polygon provides a visual representation of the overall shape and pattern of the data distribution.

Frequency Curve:
A frequency curve, also known as a frequency distribution curve or smooth curve, is a smoothed representation of the data distribution. It is constructed by plotting the cumulative frequencies or relative frequencies on the y-axis and the midpoints of the corresponding classes on the x-axis. The points are connected by a smooth curve, typically obtained by applying a mathematical technique such as interpolation or curve fitting. The frequency curve provides a more refined representation of the distribution by removing the jaggedness present in the frequency polygon.

In summary, the key differences between a frequency polygon and a frequency curve are:

A frequency polygon is constructed by connecting the midpoints of the upper sides of the histogram bars with straight lines, while a frequency curve is constructed by connecting the points with a smooth curve.
Frequency polygons provide a simpler representation of the data distribution, while frequency curves offer a smoother and more refined depiction.
Frequency polygons are appropriate for discrete or grouped data, while frequency curves are often used for continuous data.