Explanation:

The most commonly used measure of dispersion is the standard deviation. Here's why:

1. Definition:
The standard deviation measures the average distance between each data point and the mean of the dataset. It shows how spread out the values are from the mean. A higher standard deviation indicates more dispersion or variability in the data.

2. Calculation:
To calculate the standard deviation, follow these steps:
- Calculate the mean of the dataset.
- Subtract the mean from each data point and square the result.
- Calculate the average of these squared differences.
- Take the square root of the average.

3. Advantages:
The standard deviation has several advantages that make it the most commonly used measure of dispersion:
- It takes into account every data point in the dataset, making it a comprehensive measure.
- It is not affected by extreme outliers, as it squares the differences between data points and the mean.
- It provides a measure of the spread in the same units as the original data, making it easily interpretable.

4. Comparison with Other Measures:
Let's compare the standard deviation with the other options mentioned:

- Range: The range is the difference between the maximum and minimum values in the dataset. While it provides a rough estimate of dispersion, it does not consider all the data points and is highly affected by outliers. Hence, it is less reliable than the standard deviation.
- Coefficient of Variation: The coefficient of variation is the ratio of the standard deviation to the mean. It is used to compare the variability of different datasets with different means. However, it is not as commonly used as the standard deviation itself.
- Quartile Deviation: The quartile deviation is the difference between the upper quartile and lower quartile of a dataset. It provides a measure of dispersion for skewed distributions but does not take into account all the data points. Therefore, it is less commonly used than the standard deviation.

In conclusion, the standard deviation is the most commonly used measure of dispersion because it considers all the data points, is not affected by outliers, provides a measure in the same units as the original data, and is widely applicable to different types of datasets.