Quartile Coefficient of Dispersion (QCD)

The Quartile Coefficient of Dispersion (QCD) is a measure of relative dispersion or variability in a dataset. It is derived from the quartiles of the dataset and represents the spread of the data around the median.

To calculate the Quartile Coefficient of Dispersion, we need the values of Q1, Q3, and the Coefficient of SK(B).

Given:
- Coefficient of SK(B) = -0.36
- Q1 = 8.6
- Q3 = 12.3

Calculating the Quartile Coefficient of Dispersion:

Step 1: Calculate the Interquartile Range (IQR)
The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1).

IQR = Q3 - Q1
= 12.3 - 8.6
= 3.7

Step 2: Calculate the Quartile Coefficient of Dispersion (QCD)
The Quartile Coefficient of Dispersion is given by the following formula:

QCD = (Q3 - Q1) / (Q3 + Q1)

Substituting the values we have:

QCD = (3.7) / (12.3 + 8.6)
= 3.7 / 20.9
≈ 0.177

Interpreting the Quartile Coefficient of Dispersion:

The Quartile Coefficient of Dispersion (QCD) is a measure of relative dispersion in a dataset. A QCD value closer to 0 indicates low dispersion, while a value closer to 1 indicates high dispersion.

In this case, the calculated QCD value is approximately 0.177. Since it is closer to 0, we can infer that the dataset has relatively low dispersion. This means that the values in the dataset are clustered closely together around the median.

Conclusion:

The Quartile Coefficient of Dispersion (QCD) for the given dataset is approximately 0.177. This indicates low dispersion, suggesting that the values in the dataset are closely clustered around the median.