Simple Average: Formula, Rules and Solved Examples
Simple Average is the arithmetic mean of a set of values. It is calculated by dividing the total sum of all values by their number. This page explains the simple average formula, methods for finding missing values, weighted group averages, and basic average tricks through clear numerical examples.
What Is Simple Average?
For values x₁, x₂, x₃, ..., xₙ, the simple average is (x₁ + x₂ + x₃ + ... + xₙ) ÷ n. The average has the same unit as the observations. For example, the average of 8, 12 and 16 is (8 + 12 + 16) ÷ 3 = 36 ÷ 3 = 12.
Simple Average Formula & Tricks
Important Formulas
If the values are x₁, x₂, ..., xₙ, then Average = (x₁ + x₂ + ... + xₙ) ÷ n.
This formula gives the total when the average and the number of values are known.
First calculate the required total as Average × Total number of observations, then subtract the known sum.
Here, n₁ and n₂ are group sizes, while a₁ and a₂ are their respective averages.
Quick Tricks
Choose a nearby base value and add the deviations instead of adding every value directly. Average = Base value + (Sum of deviations ÷ Number of values).
If one value changes by d, the average changes by d ÷ n, where n is the total number of observations.
For a set of real numbers, the simple average cannot be less than the smallest value or greater than the largest value.
Simple Average Concepts
Finding the Average from Given Values
The count must include every observation, including repeated values. For 15, 18, 21 and 26, the sum is 80 and the number of observations is 4, so the average is 80 ÷ 4 = 20.
Finding the Total from a Known Average
If the average of 7 numbers is 24, their total is 24 × 7 = 168. This reverse form of the average formula is also used before finding a missing value.
Finding a Missing Value
If there are n values with average A, the required total is nA. For four numbers with average 18, if three numbers are 12, 17 and 20, the missing number is (4 × 18) − (12 + 17 + 20) = 72 − 49 = 23.
Effect of Adding or Removing a Value
If the original average is A for n values, the original total is nA. After adding x, the new average is (nA + x) ÷ (n + 1). After removing x, it is (nA − x) ÷ (n − 1), provided n is greater than 1.
Combined Average of Two Groups
The simple average of the two group averages is valid only when both groups have equal sizes. For unequal sizes, use group size × group average for each total.
Simple Average Video Lessons
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Average Formula, Sum and Missing Value
Learn the average formula, calculate the total sum using averages, and find missing values in average-based quantitative aptitude problems.
Practice Simple Average Questions
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Simple Average Revision Points
Use these formulas and rules to revise simple average calculations.
- Average = Sum of observations ÷ Number of observations.
- Sum = Average × Number of observations.
- For a missing value, subtract the known sum from the required total.
- Adding a value x to n observations gives new average = (nA + x) ÷ (n + 1).
- Removing a value x from n observations gives new average = (nA − x) ÷ (n − 1).
- For two groups, combined average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).
- The average of a set lies between its smallest and largest values.
- The average has the same unit as the original observations.
Simple Average FAQs
What is the simple average formula?
Simple average = Sum of all observations ÷ Number of observations. For 6, 10 and 14, the average is 30 ÷ 3 = 10.
How do you find a missing number when the average is given?
Multiply the given average by the total number of values and subtract the sum of the known values. If the average of 4 numbers is 15 and three sum to 37, the missing number is 60 − 37 = 23.
How does adding one value affect the average?
If the original average is A for n values and x is added, the new average is (nA + x) ÷ (n + 1). If A = 12, n = 5 and x = 18, the new average is 78 ÷ 6 = 13.
Can the average of two group averages be found by simply adding and dividing by 2?
Only when the two groups have equal sizes. For unequal group sizes, use Combined average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).
What is the difference between simple average and weighted average?
A simple average gives equal weight to every value. A weighted average gives different importance or weights to values and is calculated as Sum of (value × weight) ÷ Sum of weights.
What happens to the average if every observation increases by the same number?
The average also increases by that number. For example, adding 5 to every value increases the average by 5 because the total increases by 5n while the count remains n.