Understanding Quartile Deviation
The quartile deviation (QD), also known as the semi-interquartile range, is a measure of statistical dispersion that indicates the spread of the middle half of a dataset.
Definition
- QD is calculated as half the difference between the first quartile (Q1) and the third quartile (Q3):
- QD = (Q3 - Q1) / 2
Relationship with Other Measures of Dispersion
- The quartile deviation provides insight into the variability of data without being affected by extreme values.
Comparing Quartile Deviation to Other Measures
- Standard Deviation (SD): A measure of the average distance of each data point from the mean.
- Standard Deviation of a Dataset (SD): Refers to the overall standard deviation calculated for the entire dataset.
- The quartile deviation is often expressed as a fraction of the standard deviation, but the exact relationship can vary based on the dataset.
Answer to the Question
- Among the options provided:
- A. 2/3 of SD
- B. 4/5 of SD
- C. 5/6 of SD
- D. None of these
- The exact proportion of quartile deviation to standard deviation isn't fixed; it depends on the data distribution.
- Therefore, the answer is D. None of these.
Conclusion
- The quartile deviation is a useful statistic for understanding data dispersion, especially in skewed distributions. It is essential to analyze the context of the dataset to determine the appropriate measure of dispersion.