Which of the following cannot be determined graphically ?

Question

Accepted Answer

Option 2, "Median," is the correct answer because the median cannot be determined graphically in the same straightforward manner as the mode or mean. Here's a detailed explanation:

1. **Why Option 2 is Correct (Median):**
   - The median is the middle value of a data set when it is ordered from least to greatest. To find the median graphically, you would need to arrange the data in order and then identify the middle value, which is not directly visible on a standard graph like a histogram or a frequency polygon. While you can estimate the median using a cumulative frequency graph (ogive), it requires additional steps and is not as direct as determining the mode or mean.

2. **Why Option 1 is Incorrect (Mode):**
   - The mode is the value that appears most frequently in a data set. Graphically, the mode can be easily identified as the highest peak in a histogram or a frequency polygon. The mode is the most visually apparent measure of central tendency on these types of graphs, making it straightforward to determine graphically.

3. **Why Option 3 is Incorrect (Mean):**
   - The mean, or average, can be determined graphically by calculating the balance point of a distribution. While it is not directly visible on a graph, it can be inferred by considering the distribution's shape and symmetry. In a perfectly symmetrical distribution, the mean coincides with the median and mode, and its position can be estimated graphically.

4. **Why Option 4 is Incorrect (None of these):**
   - This option suggests that all measures of central tendency can be determined graphically, which is not true. As explained, the median requires additional steps and is not directly visible on standard graphs, unlike the mode and mean, which can be more readily identified or estimated.

In conclusion, Option 2 is the correct answer because the median cannot be directly determined from a graph without additional calculations or steps, unlike the mode and mean, which can be more easily identified or estimated graphically.