The mode of a distribution can be obtained graphically from:

Concept

For a continuous grouped frequency distribution, the mode is the value around which observations are most concentrated. A histogram represents each class interval by an adjacent rectangle whose area is proportional to frequency; for equal class widths, the rectangle height is proportional to frequency. This makes it possible to identify the modal class and locate the mode graphically.

Application

Among the given graphical forms, a histogram directly displays the class frequencies needed for this construction. Therefore, the mode of the distribution can be obtained graphically from a histogram.

Cross-check and contrast

• A more-than-type ogive shows descending cumulative frequencies, while a less-than-type ogive shows increasing cumulative frequencies; these curves are commonly used to locate the median and other partition values.

• A frequency polygon joins frequency points at class marks and shows the shape of a distribution, but it is not the standard graphical construction for locating the mode.

• The histogram alone supplies adjacent class rectangles and a modal class, so it satisfies the graphical requirement in the stem.

Result: Histogram.