Welcome to our online Average Calculator, your go-to tool for simplifying numerical computations. Dive in and explore the ease of mathematical computations at your fingertips!
* SD = standard deviation
Calculating the Average
The average, also known as the arithmetic mean, is determined by adding up all the values (a1, a2, ... an) in a dataset and dividing the sum by the total count (n).
Example: For the numbers 1, 2, and 5, the average is calculated as follows: Average = (1 + 2 + 5) / 3 = 2.667
Weighted Average Calculation
To calculate the weighted average (x), sum the products of the weight (wi) and the corresponding data number (xi), then divide this sum by the total sum of weights.
Example: Let's find the weighted average for class grades with equal weight: 70, 70, 80, 80, 80, and 90.
Since all grades have equal weight, we can either calculate a simple average or, to consider the frequency of each grade, use a weighted average.
2 × 70, 3 × 80, 1 × 90
x = (2 × 70 + 3 × 80 + 1 × 90) / (2 + 3 + 1) = 470 / 6 = 78.33333
The average serves as a valuable representative value for large datasets, such as determining the average number of customers over a specific period in a business context.