A statistical measure which can not be determine graphically is :

Question

Accepted Answer

Option 4, Harmonic Mean, is the correct answer because it is a statistical measure that cannot be determined graphically. Here's a detailed explanation:

1. **Harmonic Mean (Option 4)**:
   - The harmonic mean is a type of average, specifically the reciprocal of the arithmetic mean of the reciprocals of a set of numbers. It is primarily used in situations where average rates are desired, such as speeds or densities.
   - Unlike the mode, mean, or median, the harmonic mean does not have a straightforward graphical representation. It requires a specific calculation involving reciprocals, which cannot be directly visualized on common statistical graphs like histograms or box plots.

2. **Mode (Option 1)**:
   - The mode is the value that appears most frequently in a data set. It can be easily identified on a graph, such as a histogram or a frequency distribution plot, as the peak or highest bar. Therefore, it can be determined graphically.

3. **Mean (Option 2)**:
   - The mean, or arithmetic average, is the sum of all data points divided by the number of points. It can be represented graphically, for example, by the balance point of a distribution on a histogram or by a line on a box plot indicating the average value.

4. **Median (Option 3)**:
   - The median is the middle value of a data set when it is ordered from least to greatest. It can be determined graphically using a box plot, where it is represented by the line inside the box, or by identifying the point that divides the area under a distribution curve into two equal halves.

In summary, while the mode, mean, and median can all be determined graphically through various types of plots and charts, the harmonic mean requires a specific mathematical calculation that does not lend itself to direct graphical representation. This makes Option 4 the correct answer.