Skewness and Kurtosis

​Quartile Deviation

The range and quartile deviation are measures of dispersion that depend on the values of the variables at a particular position in the distribution. The range is based on extreme values in the distribution. It does not consider the deviation among the values. In order to study the variation among the values, the measure of inter-quartile range is used.

Inter-Quartile Range = Third Quartile − First Quartile
                                  = Q₃ − Q₁

Quartile deviation is the half of the difference between third quartile, Q₃ and first quartile, Q₁ of the series.

∴ Quartile deviation = $\frac{Q_3-Q_1}{2}$

Quartile deviation gives half of the range of middle 50% observations. Quartile deviation is also known as semi-inter-quartile range.

Calculation of quartile deviation

1. For an individual series, the first and third quartiles can be calculated using the following formula:

Q₁ = Value of $\frac{\left(n+1\right)}{4}$th ordered observation

Q₃ = Value of $\frac{3\left(n+1\right)}{4}$th ordered observation

2. For a discrete series, the first and third quartiles can be calculated using the following formula:

If N = ${\sum }_{}f$, then

Q₁ = Value of $\frac{\left(N+1\right)}{4}$th ordered observation

Q₃ = Value of $\frac{3\left(N+1\right)}{4}$th ordered observation

3. For a continuous series, the first and third quartiles can be calculated using the following formula:

$Q_1=L+\left(\frac{{\displaystyle \frac{N}{4}}-\mathrm{c}.\mathrm{f}.}{f}\right)\times h$

$Q_3=L+\left(\frac{{\displaystyle \frac{3N}{4}}-\mathrm{c}.\mathrm{f}.}{f}\right)\times h$

Here, L = lower limit of the quartile class

f = frequency of the quartile class

h = class interval of quartile class

c.f. = total of all the frequencies below the quarti…