# Frequency Polygon vs Histogram

-

Frequency Polygons and Histograms are both two different ways of graphically presenting data given in the form of a frequency distribution. The frequency polygon can represent both grouped and ungrouped (discrete) data whereas a histogram can only be constructed for grouped frequency distribution.

In the case of discrete frequency distribution, a frequency polygon is obtained by plotting the frequencies on the vertical axis (Y-axis) against the corresponding values of the variable on the horizontal axis (X-axis) and joining the points so obtained by straight lines.

In the case of a grouped or continuous frequency distribution, a frequency polygon may be drawn using a histogram. First, draw the histogram of the given frequency distribution and then join the mid-points of the tops (upper horizontal sides) of the adjacent rectangles of the histogram by a straight-line graph. The figure so obtained is called a frequency polygon.

We now explain some of the main differences between frequency polygons and histograms.

### Difference between Frequency Polygons and Histograms:

1. Frequency polygons can be used to visualize discrete ungrouped data whereas a histogram can only be used to represent grouped frequency distributions.
2. The histogram is a two-dimensional figure, that is, a collection of adjacent rectangles whereas the frequency polygon is a line graph.
3. Frequency polygon can be used more effectively for the comparative study of two or more frequency distributions because frequency polygons of different distributions can be drawn on the same single graph. This is not possible in the case of histograms where we need separate histograms for each of the frequency distributions.
4. For studying the relationship of the individual class frequencies to the total frequency, the histogram gives a better picture and is accordingly preferred over the frequency polygon.
5. Unlike histograms, a frequency polygon is a continuous curve and therefore possesses all the distinct advantages of graphical representations, that is, it may be used to determine the slope, rate of change, estimates (interpolation and extrapolation), etc., wherever admissible.
6. One point of similarity between histogram and frequency polygon is that they cannot be constructed for frequency distributions with open-end classes. Also, suitable adjustments are required for frequency distributions with unequal classes.

#### References

Business Statistics – SC Gupta and Indra Gupta.