The coefficient of dispersion based on quartiles of the given set of data is known as the coefficient of quartile deviation.
Formula of Coefficient of Quartile Deviation:
The coefficient of quartile deviation can be calculated using the formula,
Coefficient of Quartile Deviation = (Q3-Q1)/(Q3+Q1).
- Q3 denotes the upper quartile.
- Q1 denotes the lower quartile.
Interpretation:
Notice that in the above formula, the numerator is always less than the denominator. In particular, this implies that the value of the coefficient is always less than 1.
In fact, the coefficient always lies between 0 and 1. The closer the value of the coefficient is to 1 the greater the degree of spread/variation in the data.
Example:
Consider the following series of data values: 21, 25, 28, 32, 36, 57, 59, and 63.
Since we have 8 data values we have that N=8. We first calculate the upper and lower quartiles as follows,
Lower Quartile Q1 = (N/4)th term = (8/4) th term = 2nd term = 25.
Upper Quartile Q3 = (3N/4)th term = (3*8/4) th term = 6th term = 57.
We now calculate the coefficient of quartile deviation using the formula,
Coefficient of Quartile Deviation = (Q3-Q1)/(Q3+Q1)
= (57-25)/(57+25) = 32/82 = 0.3902.
Since the value of the coefficient for this data set is closer to 0 compared to 1, we conclude that the above data set has a lesser degree of dispersion/variation.
