The definition of Mode fails if:

Options

A. the maximum frequency is repeated
B. the maximum frequency is not repeated
C. the maximum frequency occurs in the middle
D. the curve drawn with the help of given data is symmetrical

Explanation

To determine when the definition of mode fails, we need to analyze the characteristics of the mode and the conditions under which it becomes undefined or ambiguous.

### Step-by-Step Solution:

1. **Understanding Mode**:
- The mode is defined as the value that appears most frequently in a data set. It represents the highest frequency of occurrence.

2. **Symmetrical Distribution**:
- A symmetrical distribution is one where the left side of the distribution mirrors the right side. Common examples include the normal distribution (bell curve).

3. **Frequency in Symmetrical Distributions**:
- In a symmetrical distribution, the frequencies of the values on either side of the center (mean) are balanced. This means that there may not be a single value that occurs more frequently than others.

4. **Multiple Modes**:
- In some symmetrical distributions, there can be multiple values that occur with the same highest frequency, leading to a situation known as multimodal distribution. In such cases, it becomes difficult to identify a single mode.

5. **Conclusion**:
- The definition of mode fails when the data forms a symmetrical distribution because there is no distinct value that can be identified as the mode. The lack of a clear highest frequency means that the mode is either undefined or ambiguous.

### Final Answer:
The definition of mode fails when the data is symmetrically distributed, as there may not be a single most frequently occurring value.

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