Dispersion Measure Using All Scores

A measure of dispersion quantifies the spread or variability within a set of data. Different measures consider different aspects of the data's distribution.

Analyzing Dispersion Measures

The question asks for the specific measure of dispersion that utilizes all the scores in a dataset for its calculation. Let's examine the options:

• Range: This is calculated as the difference between the maximum and minimum values (Max - Min). It only considers two scores, ignoring all others.
• Quartile Deviation (QD): Calculated as QD = (Q3 - Q1) / 2, where Q1 and Q3 are the first and third quartiles. This measure focuses on the spread of the middle 50% of the data and does not consider all scores.
• Average Deviation (AD): Also known as Mean Absolute Deviation (MAD), it's the average of the absolute differences between each data point and the mean. The formula is AD = $\sum_{i=1}^{n} |x_i - \bar{x}| / n$. Since it sums the deviations of *every* score ($x_i$) from the mean ($\bar{x}$), it considers all scores.
• Inter-quartile Range (IQR): This is simply the difference between the third and first quartiles (IQR = Q3 - Q1). Like Quartile Deviation, it focuses only on the central 50% of the data and ignores scores outside this range.

Conclusion

Based on the analysis, the Average Deviation is the only measure listed that inherently incorporates every score from the dataset into its calculation.