It is often convenient to have one number that represent the whole data. Such a number is called a ==Measures of Central Tendency.==
The most common among them are
- Arithmetic Mean
- Median
- Mode
Arithmetic Mean
The arithmetic mean, commonly referred to as the average, is a measure of central tendency.
$\text{Arithmetic Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$
==Measures of Dispersion==
Measures of dispersion describe how spread out the values in a data set are. They give us an idea of the variability or consistency within the data.
Here are the most common measures of dispersion:
- Range
- Mean deviation
- Quartile deviation
- Standard deviation
- Variance
- Coefficient of Variation
Range
Definition: The range is the difference between the highest and lowest values in a data set.
$ \text{Range} = \text{Max value} - \text{Min value} $
The coefficient of range is a measure of relative dispersion, which compares the spread of a data set to its size.
$\text = \frac{\text{Range}}{\text{Max value} + \text{Min value}}$
Mean Deviation
(also known as the Mean Absolute Deviation, or MAD) is a measure of dispersion that indicates the average distance of each data point from the mean of the data set. Unlike variance and standard deviation, mean deviation uses absolute values, making it less sensitive to extreme values or outliers.
$\text{Mean Deviation} = \frac{\sum_{i=1}^{n} |x_i - \overline{x}|}{n} $
$( x_i ) \text { represents each individual data point.}$
$( \overline{x} ) \text { is the mean of the data set.}$