Consider the following
statements 1 Range is not a good measure of dispersion
2 Range is highly affected by the existence of extreme values Which one of the following is correct in respect of the above statements?

Options

A. Both statements 1 and statements 2 are correct and statement 2 is the correct explanation of statement 1.
B. Both statements I and statement 2 are correct but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is correct but statement 2 is not correct.
D. Statement 2 is correct but statement is not correct.

Answer

To solve the question, we need to analyze the two statements provided regarding the range as a measure of dispersion.

### Step-by-Step Solution:

1. **Understanding Dispersion**:
- Dispersion refers to the extent to which data values in a dataset differ from each other and from the average (mean). Common measures of dispersion include range, variance, and standard deviation.

**Hint**: Remember that dispersion helps us understand how spread out the data is.

2. **Analyzing Statement 1**:
- The first statement claims that "Range is not a good measure of dispersion."
- The range is calculated as the difference between the maximum and minimum values in a dataset. While it provides a quick sense of spread, it does not account for how values are distributed between the extremes.

**Hint**: Consider why a single value (like range) might not capture the overall spread of data effectively.

3. **Analyzing Statement 2**:
- The second statement asserts that "Range is highly affected by the existence of extreme values."
- This is true because if there are extreme values (outliers) in the dataset, they can significantly alter the maximum and minimum values, thus affecting the range.

**Hint**: Think about how changing the highest or lowest value in a dataset impacts the range.

4. **Conclusion**:
- Both statements are correct. Statement 1 accurately reflects that the range is not a comprehensive measure of dispersion, while Statement 2 explains why this is the case—because the range is sensitive to extreme values.
- Therefore, both statements are correct, and Statement 2 serves as a valid explanation for Statement 1.

**Final Answer**: Both statements are correct, with Statement 2 being the correct explanation of Statement 1.