Measures of absolute variability deals with the dispersion of the data points. This include the following:

The range is computed using the function

The range returned the minimum and maximum values of the data which are 150 and 169, respectively. And for the interquartile range, the output returned is the difference between the third and first quartiles. For quartile deviation, the formula is given by$$QD=\frac{Q_3-Q_1}{2}$$where:

Implies,

Lastly, the mean deviation$$AD=\displaystyle\frac{\displaystyle\sum_{i=1}^{n}\left|X_i-\bar{X}\right|}{n-1}$$where:

And therefore, the average deviation of the heights is,

###

Asaad, Abubakar S. (2011).

- Range -
`range`

; - Interquartile Range -
`IQR`

; - Quartile Deviation;
- Average Deviation; and,
- Standard Deviation -
`sd`

.

**Example 1**. The heights (in centimetres) of the 17 BS Stat students in section A23 of Statistical Inference under Dr. Supe were recorded. The data are the following: 151, 160, 162, 155, 154, 154, 153, 168, 169, 153, 158, 166, 152, 157, 150, 169, and 167. Compute the range, interquartile range, quartile deviation, average deviation, and standard deviation.The range is computed using the function

`range`

, while the interquartile range is obtained by `IQR`

. Thus,The range returned the minimum and maximum values of the data which are 150 and 169, respectively. And for the interquartile range, the output returned is the difference between the third and first quartiles. For quartile deviation, the formula is given by$$QD=\frac{Q_3-Q_1}{2}$$where:

- $QD$ - quartile deviation;
- $Q_3$ - third quartile; and,
- $Q_1$ - first quartile.

Implies,

Lastly, the mean deviation$$AD=\displaystyle\frac{\displaystyle\sum_{i=1}^{n}\left|X_i-\bar{X}\right|}{n-1}$$where:

- $AD$ - average deviation;
- $X_i$ - $i^{th}$ individual observations;
- $\bar{X}$ - sample mean; and,
- $n$ - total number of observations.

And therefore, the average deviation of the heights is,

###
**Reference**

Asaad, Abubakar S. (2011).*Simplified Biostatistics*. Manila: Rex Book Store, Inc.
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