Average Calculator - Calculate Mean, Median, Mode, Standard Deviation

Average Calculator - Calculate Mean, Median, Mode & More

Our free online average calculator helps you calculate various statistical measures from your data set. Whether you need to find the arithmetic mean, geometric mean, median, mode, or standard deviation, our calculator provides instant results with step-by-step calculations.

What is an Average?

An average (arithmetic mean) is a measure of central tendency that represents the typical value in a data set. It's calculated by adding all values together and dividing by the number of values. The formula is:

Average = Sum of all values / Number of values

Types of Averages and Statistical Measures

1. Arithmetic Mean (Average)

The most common type of average, calculated by summing all values and dividing by the count.

Example: For numbers 1, 2, 5, 2, 6, 6

Average = (1+2+5+2+6+6) / 6 = 22 / 6 = 3.67

2. Geometric Mean

The nth root of the product of n numbers. Useful for calculating average growth rates and ratios.

Formula: Geometric Mean = (x₁ × x₂ × ... × xₙ)^(1/n)

3. Root Mean Square (RMS)

The square root of the arithmetic mean of the squares of the values. Commonly used in physics and engineering.

Formula: RMS = √[(x₁² + x₂² + ... + xₙ²) / n]

4. Median

The middle value when data is arranged in ascending order. For even number of values, it's the average of the two middle values.

5. Mode

The value that appears most frequently in the data set. A data set can have multiple modes or no mode at all.

6. Standard Deviation

A measure of how spread out the data is from the mean. There are two types:

Population Standard Deviation: Used when you have data for the entire population
Sample Standard Deviation: Used when you have a sample of the population

Weighted Average

A weighted average gives different weights to different values based on their importance or frequency. It's calculated as:

Weighted Average = (w₁×x₁ + w₂×x₂ + ... + wₙ×xₙ) / (w₁ + w₂ + ... + wₙ)

Example: Class grades with different weights

2 students got 70, 3 students got 80, 1 student got 90

Weighted Average = (2×70 + 3×80 + 1×90) / (2+3+1) = 470 / 6 = 78.33

How to Use Our Average Calculator

Enter your data: Input numbers separated by spaces, commas, or semicolons
Click Calculate: Get instant results for all statistical measures
View step-by-step calculation: See how the average is calculated
Use weighted average: Toggle the weighted average section for weighted calculations

Common Use Cases

Academic: Calculate grade point averages and test scores
Business: Analyze sales data, customer ratings, and performance metrics
Research: Statistical analysis and data interpretation
Finance: Calculate average returns, prices, and financial ratios
Sports: Player statistics and team performance analysis

Tips for Accurate Calculations

Ensure all data points are numeric values
Remove any outliers that might skew your results
Use appropriate decimal places for your context
Consider whether you need population or sample standard deviation
For weighted averages, ensure weights are proportional to importance

Frequently Asked Questions

What's the difference between mean, median, and mode?

The mean is the arithmetic average, median is the middle value, and mode is the most frequent value. Each provides different insights about your data's central tendency.

When should I use weighted average instead of regular average?

Use weighted average when different data points have different levels of importance or when you need to account for varying sample sizes or frequencies.

What's the difference between population and sample standard deviation?

Population standard deviation is used when you have data for the entire population, while sample standard deviation is used for a sample of the population and includes a correction factor (n-1 instead of n).

Can I calculate averages for negative numbers?

Yes, our calculator handles negative numbers, decimals, and any real numbers. The calculations work the same way regardless of whether the numbers are positive or negative.

How accurate are the calculations?

Our calculator provides results with 6 decimal places of precision, which is suitable for most practical applications. The calculations use standard mathematical formulas for maximum accuracy.