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Statistics Calculator

StatisticValue
Count-
Sum-
Mean (Average)-
Median-
Mode-
Largest-
Smallest-
Range-
Geometric Mean-
Standard Deviation-
Variance-
Sample Standard Deviation-
Sample Variance-
Sorted data: -

Formulas and Examples

Mean: Sum / Count

Example: For numbers 2, 10, 23, 38
Sum = 2 + 10 + 23 + 38 = 73
Count = 4
Mean = 73 / 4 = 18.25

Median: Middle value(s) of sorted list

Example: For sorted numbers 2, 10, 23, 38
Median = (10 + 23) / 2 = 16.5
For odd count: 2, 10, 23 → Median = 10

Mode: Most frequent value(s)

Example: For numbers 2, 10, 10, 23, 38
Mode = 10 (appeared 2 times)
Multiple modes possible if same frequency

Standard Deviation: √(Σ(x - mean)² / n)

Example: For numbers 2, 10, 23, 38 (mean=18.25)
Variance = [(2-18.25)² + (10-18.25)² + (23-18.25)² + (38-18.25)²]/4 = 175.6875
Standard Deviation = √175.6875 ≈ 13.25
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This simple and intuitive statistics calculator helps you compute key statistical values including the mean, sample standard deviation, population standard deviation, and geometric mean. It’s great for quick calculations and general statistical analysis.

For more in-depth explanations and examples, explore the related calculators linked throughout the site.

Although the variance isn’t shown directly, it is calculated automatically. Just remember:
Variance = (Standard Deviation)²
Make sure you’re using the right type of standard deviation:

  • s for sample standard deviation

  • σ for population standard deviation

Then square that value to get the variance.

Understanding the Geometric Mean

The geometric mean is a type of average that reflects central tendency by multiplying all numbers in a data set and taking the root based on how many values there are.

Unlike the arithmetic mean, which uses addition, the geometric mean uses multiplication, making it better for comparing values across different scales or measuring percentage growth.

Why Use Geometric Mean?

Consider this example:
You’re comparing two metrics—fuel efficiency (0–5 scale) and safety (0–100 scale). If you use the arithmetic mean, the higher-scale value (safety) may dominate the result. For instance:

  • Fuel efficiency goes from 2 to 5 (a 150% increase)

  • Safety goes from 80 to 85 (a 6.25% increase)

But with the arithmetic mean, the small change in safety could outweigh the big improvement in fuel efficiency. The geometric mean corrects this by treating relative changes equally.

Geometric Mean Formula

To calculate the geometric mean:

Geometric Mean = (x₁ × x₂ × x₃ × … × xₙ)^(1/n)

Where:

  • x₁ to xₙ are the individual values

  • n is the total number of values

  • The product (×) is taken over all the values

Example Calculation

For the data set: 1, 5, 7, 9, 12

  1. Multiply all values:
    1 × 5 × 7 × 9 × 12 = 3780

  2. Take the 5th root of 3780:
    Geometric Mean ≈ 4.62

(Use a root calculator if you need help computing nth roots.)

Where It’s Used

The geometric mean is valuable in various fields:

  • Finance – to calculate average growth rates

  • Statistics – for normalized or skewed data sets

  • Geometry – for ratios and area comparisons

  • Social Sciences – to analyze proportional changes

It provides a balanced average that avoids distortion caused by extreme values or varied scales, making it a smart alternative to the arithmetic mean in many situations.

Mathematics Calculators