Identifying Statistical Measures of Dispersion

Statistical methods can be broadly categorized. Some describe the central point of data (central tendency), while others describe the spread or variability of data (dispersion).

Measures of Dispersion Defined

• Measures of Dispersion: Quantify the amount of variability or spread in a set of data.
• Measures of Central Tendency: Indicate the center or typical value of a dataset.

Analysis of Options

Let's analyze the given statistical terms:

• A. Range: Calculated as the difference between the maximum and minimum values in a dataset ($Max - Min$). It directly measures the total spread. Thus, it's a measure of dispersion.
• B. Variance: Measures the average squared difference of each data point from the mean. A higher variance indicates greater spread. Thus, it's a measure of dispersion. The formula involves: $ \sigma^2 = \frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N} $
• C. Mean: Represents the average value of the dataset ($Sum of values / Number of values$). It is a measure of central tendency, not dispersion.
• D. Standard Deviation: The square root of the variance ($ \sigma = \sqrt{\sigma^2} $). It measures the average deviation of data points from the mean in the original units. Thus, it's a measure of dispersion.

Conclusion

Based on the definitions, Range (A), Variance (B), and Standard Deviation (D) are measures of dispersion. The Mean (C) is a measure of central tendency.

Therefore, the correct set of measures of dispersion is A, B, D only.

This corresponds to Option 4.