Average
Arithmetic mean, weighted averages
Average is a fundamental mathematical concept that represents the central value of a set of numbers. In competitive exams, average problems test your ability to manipulate data sets, understand weighted distributions, and handle scenarios involving additions, removals, and replacements of values in a collection.
Key formulas and rules
Key concepts
Simple Arithmetic Mean
The basic average is calculated by dividing the sum of all observations by the number of observations. This is the most common form of average and applies to situations where all values have equal importance. For a set {a , a , ..., an}, the average = (a + a + ... + an) / n.
Weighted Average
When different values have different weights or importance, use weighted average. Formula: Weighted Average = (w x + w x + ... + wnxn) / (w + w + ... + wn), where w represents weights and x represents values. Common applications include calculating average marks with different subject weightings, average prices of mixed quantities, and portfolio returns.