Which of the following can not be determined by Graphic method?

Question

Accepted Answer

The correct option is 1:

The Mean, or the arithmetic average, is the only measure of central tendency among the given options that cannot be determined accurately using standard graphical methods in statistics. The mean requires the specific value of every observation in the dataset (or the midpoint of every class interval in grouped data) to calculate its precise value. Since graphic representations like histograms, frequency curves, or ogives illustrate the distribution and frequency of data rather than the precise numerical contribution of each value, they lack the necessary arithmetical detail needed for mean calculation. The mean is a mathematically defined measure, requiring summation and division, which graphs cannot replicate.

The incorrect option is 2 (Median):
The median can be accurately determined graphically by drawing "less than" and "more than" cumulative frequency curves (ogives). The point where these two ogives intersect corresponds to the median value on the X-axis, making it a reliable graphical measure of central tendency.

The incorrect option is 3 (Mode):
The mode can be determined graphically by using a histogram. The mode is found by drawing lines connecting the top corners of the highest frequency rectangle (the modal class) to the corners of the adjacent rectangles, and the intersection of these lines gives the modal value on the X-axis.

The incorrect option is 4 (Quartiles):
Quartiles, along with the median (which is the second quartile), are positional averages and can be easily found using the cumulative frequency curve (ogive). Once the ogive is plotted, we locate the required quartile position (e.g., N/4 for Q1 or 3N/4 for Q3) on the Y-axis, move horizontally to the curve, and drop vertically to the X-axis to find the quartile value.