Which average can not be calculated with the help of graphical method ?

Q: Which average can not be calculated with the help of graphical method ?

Which average can not be calculated with the help of graphical method ?

Question

Accepted Answer

The correct option is 2:
The **Mean** (or Arithmetic Average) cannot be calculated with the help of a graphical method because its computation is inherently mathematical, requiring the explicit sum of all observations divided by the total number of observations. Graphical representations, such as histograms or ogives, primarily depict frequency distribution or cumulative frequency, which do not preserve the exact magnitude or sum of all individual values needed for this precise arithmetic calculation. The mean is sensitive to the exact value of every observation, a detail that is lost when data is grouped for graphical presentation. Hence, the true value of the mean must be calculated using the mathematical formula, making it a strictly algebraic measure.

The incorrect option is 1:
The **Median** is a positional average and can be accurately determined using the **Ogive curve** (the cumulative frequency curve). By locating the position of the middle item (N/2) on the cumulative frequency (Y-axis), a horizontal line is drawn to the ogive, and a perpendicular dropped to the X-axis reveals the median value. This graphical technique is a fundamental part of descriptive statistics.

The incorrect option is 3:
The **Mode** is the measure of central tendency that represents the value occurring most frequently, and it can be visually and accurately determined from a **Histogram**. Once the histogram is drawn, the modal value is found by identifying the highest bar (the modal class). A simple geometrical construction involving drawing diagonal lines across the top of the modal bar and its adjacent bars, with a perpendicular dropped from the intersection point to the X-axis, provides the mode.

The incorrect option is 4:
**Quartiles** are partition values that divide the data set into four equal parts. Since they are positional in nature, they use the same methodology as the median and are also accurately calculated using the **Ogive curve**. Specifically, the first quartile (Q1) is determined at the (N/4)th item and the third quartile (Q3) is determined at the (3N/4)th item on the cumulative frequency curve. Therefore, they are readily found using this graphical technique.