Arithmetic Mean The arithmetic mean, also known as the average, is a measure of the central tendency of a set of numerical data points. It is calculated by...
Arithmetic Mean
The arithmetic mean, also known as the average, is a measure of the central tendency of a set of numerical data points. It is calculated by summing all the numbers in the set and dividing the sum by the total number of numbers.
Formal Definition:
The arithmetic mean, denoted by the symbol (\bar{x}), of a set of numbers (x_1, x_2, \cdots, x_n) is defined as:
where (n) is the total number of numbers in the set.
Examples:
If a set of numbers is {10, 15, 20, 25}, the arithmetic mean would be (10 + 15 + 20 + 25) / 4 = 18.
If a set of numbers is {2, 4, 6, 8}, the arithmetic mean would be 6.
Properties of the Arithmetic Mean:
The arithmetic mean is a scalar, meaning it is a single number.
The arithmetic mean is independent of the order of the numbers in the set.
The arithmetic mean is a measure of central tendency, meaning it is a point that lies in the center of the data distribution.
The arithmetic mean is a consistent measure, meaning that it has the same value for all subsets of the original set