Coefficient of Quartile Deviation (Q.D) is a measure of relative variability and is used to compare the dispersion of different datasets. It is calculated as the ratio of the Quartile Deviation to the Median.

Given:
Mean = 5
Standard Deviation (S.D) = 2.6
Median = 5
Quartile Deviation (Q.D) = 1.5

To find the Coefficient of Q.D, we need to calculate the Quartiles first.

Quartiles:
Quartiles divide the data into four equal parts, where the first quartile (Q1) represents the 25th percentile, the second quartile (Q2) represents the 50th percentile (which is the median), and the third quartile (Q3) represents the 75th percentile.

Since the Median is given as 5, it represents the second quartile (Q2).

Mean and Standard Deviation:
Mean represents the average value of the dataset and is given as 5.
Standard Deviation measures the dispersion or spread of the dataset around the mean and is given as 2.6.

Coefficient of Quartile Deviation Calculation:
1. Calculate the Quartile Deviation (Q.D):
Q.D = (Q3 - Q1) / 2
Given Q.D = 1.5

2. Calculate the Coefficient of Quartile Deviation:
Coefficient of Q.D = Q.D / Median
Coefficient of Q.D = 1.5 / 5 = 0.3

Therefore, the Coefficient of Quartile Deviation is 0.3 or 30%.

In this case, the Coefficient of Quartile Deviation is a relative measure of the variability of the dataset. A coefficient of 0.3 indicates that the Quartile Deviation is 30% of the Median, suggesting a moderate dispersion of the data.

It is important to note that the Coefficient of Quartile Deviation is a dimensionless measure and is useful in comparing the variability of different datasets. A higher coefficient indicates a greater dispersion, while a lower coefficient indicates a lesser dispersion.