**Measures of Absolute Dispersion**

**Absolute dispersion** measures indicate the extent to which data values deviate from a central point, such as the mean or median. They help us determine the degree of variability within a dataset.

**Range**

The **range** of a dataset is the difference between the highest and lowest values. It is the simplest measure of dispersion.

$text{Range} = L – S$

Where $L$ is the largest value, and $S$ is the smallest value in the dataset.

**Inter-Quartile Range (IQR)**

The **Inter-Quartile Range (IQR)** is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$).

$text{IQR} = Q_3 – Q_1$

It is a measure of variability that indicates the spread of the middle 50% of the data.

**Mean Deviation**

The **mean deviation** is the average of the absolute deviations from a central value. It can be calculated about the mean, median, or mode.

1. Mean deviation about the mean ($MD(bar{x})$):

$MD(bar{x}) = frac{sum |x – bar{x}|}{n}$

2. Mean deviation about the median ($MD(m_d)$):

$MD(m_d) = frac{sum |x – m_d|}{n}$

3. Mean deviation about the mode ($MD(m_o)$):

$MD(m_o) = frac{sum |x – m_o|}{n}$

**Quartile Deviation (Q)**

The **quartile deviation** is half the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$).

$QD = frac{Q_3 – Q_1}{2}$

**Variance and Standard Deviation**

**Variance ($sigma^2$)** measures the average of the squared deviations from the mean:

$sigma^2 = frac{sum (x – bar{x})^2}{n}$

**Standard Deviation ($sigma$)** is the square root of the variance:

$sigma = sqrt{frac{sum (x – bar{x})^2}{n}}$