Math & StatisticsVerified: 2026-10-05
Average Calculator
Calculate arithmetic mean, median, mode, geometric mean, range, sum, count, and standard deviation for any dataset with instant step-by-step statistics.
Direct Answer:The average (arithmetic mean) is calculated by adding all the numbers in a dataset together and dividing the sum by the count of numbers (Mean = Sum ÷ Count). For example, the average of 10, 25, 30, 45, and 90 is (200 ÷ 5) = 40.
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Adjust Parameters
Separate numbers using commas, spaces, tabs, semicolons, or newlines.
Quick Datasets:
Ordered Dataset (5 values)
1025304590
Average (Arithmetic Mean)
40
Based on 5 data points (Sum = 200)
The average is calculated as 200 ÷ 5 = 40.
Median (Middle Value)
30
Mode (Most Frequent)
No unique mode
Sum (Total Added)
200
Count of Numbers (N)
5
Range (10 to 90)
80
Geometric Mean
31.3692
Sample Std Dev (s)
30.6186
Population Std Dev (σ)
27.3861
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How Average Calculator is Calculated
Transparent mathematical formulas and assumptions used across our financial engines.
Mathematical Formula
\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i \quad | \quad \text{Median} = \text{Middle value of sorted dataset}
Variables & Legend
\bar{x}
Arithmetic Mean
n
Sample Count
\sum x_i
Sum of Values
s
Sample Std Dev
Step-by-Step Calculation
- Sum All Numbers:
\sum x_i = x_1 + x_2 + \dots + x_nAdd all input values together.
- Count Data Points:
n = \text{total items}Count the number of valid numerical entries.
- Divide Sum by Count:
\bar{x} = \text{Sum} / nDivide the sum by the count to determine the arithmetic mean.
- Sort for Median & Mode:
x_{(1)} \le x_{(2)} \le \dots \le x_{(n)}Order the numbers to identify the central median and most frequent mode.
Conventions & Assumptions
- The arithmetic mean is sensitive to extreme outliers; inspect the median when working with skewed data (like salaries).
- Geometric mean is computed when all values are positive, ideal for growth rates and investment returns.
- Sample standard deviation uses Bessel's correction (n - 1) in the denominator.
Frequently Asked Questions
The mean is the calculated arithmetic average (Sum ÷ Count). The median is the middle value when all numbers are ordered from smallest to largest. The mode is the most frequently occurring number in the dataset.