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.
Where is the largest value, and is the smallest value in the dataset.
- Inter-Quartile Range (IQR)
The Inter-Quartile Range (IQR) is the difference between the third quartile () and the first quartile ().
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 ():
2. Mean deviation about the median ():
3. Mean deviation about the mode ():
- Quartile Deviation (Q)
The quartile deviation is half the difference between the third quartile () and the first quartile ().
- Variance and Standard Deviation
Variance () measures the average of the squared deviations from the mean:
Standard Deviation () is the square root of the variance: