Statistics Calculator
Descriptive statistics, histogram, z-scores & percentile lookup — paste any dataset and get instant insights
Enter your dataset to begin
Paste numbers in the sidebar separated by commas, spaces, or newlines. Supports any size dataset.
Understanding the Statistics
Sample vs Population
Use Sample when your data is a subset of a larger group (divides by n−1). Use Population when you have the complete dataset (divides by n). The sample formula corrects for bias in estimating the true standard deviation.
What is Standard Deviation?
Standard deviation measures how spread out values are from the mean. A low std dev means values are close to the average; a high std dev means they are widely scattered. About 68% of values fall within ±1 std dev in a normal distribution.
Skewness & Kurtosis
Skewness describes asymmetry: positive means a longer right tail, negative means a longer left tail. Kurtosis (excess) describes tail heaviness: positive means heavier tails than a normal distribution; negative means lighter tails.
What is Statistics Calculator?
Statistics is the branch of mathematics concerned with collecting, organising, analysing, and interpreting numerical data. The basic descriptive statistics — mean, median, mode, range, variance, and standard deviation — form the foundation of data analysis and are used in virtually every quantitative field: science, economics, medicine, engineering, social sciences, sports analytics, and quality control.
Understanding the difference between these measures is important. The mean (average) is sensitive to outliers — a single very large or very small value can skew it significantly. The median (the middle value) is resistant to outliers and better represents the "typical" value in skewed distributions. The mode (most frequent value) is useful for categorical data. Standard deviation measures how spread out the values are around the mean — a low standard deviation means values cluster closely around the mean, while a high value means they are spread widely.
Altairys's Statistics Calculator accepts a list of numbers and instantly computes all key descriptive statistics: count, sum, mean, geometric mean, harmonic mean, median, mode, range, variance (population and sample), standard deviation (population and sample), coefficient of variation, quartiles (Q1, Q2, Q3), interquartile range (IQR), and outlier detection. Results include a frequency distribution table and a step-by-step explanation for each calculation.
How to Use Statistics Calculator
- Enter your numbers
Type or paste your dataset — separate values with commas, spaces, or new lines.
- Get instant results
All statistics calculate automatically as you type — mean, median, mode, and more.
- Explore the distribution
View the frequency distribution table and histogram to understand your data shape.
- Copy results
Copy any statistic or the full results table to clipboard.
Key Benefits
From basic mean/median to variance, IQR, outliers, quartiles and more.
Visual frequency distribution shows the shape of your dataset at a glance.
Each statistic shows the formula and calculation steps for learning.
Your data is analysed locally — never sent to any server.
Frequently Asked Questions
Population standard deviation (σ) is used when you have data for the entire group. Sample standard deviation (s) is used when you have a sample and want to estimate the population — it divides by (n-1) instead of n to correct for bias. For large datasets, the difference is negligible.
The IQR is the range of the middle 50% of your data. It equals Q3 (75th percentile) minus Q1 (25th percentile). The IQR is used to detect outliers: values more than 1.5 × IQR below Q1 or above Q3 are considered outliers.
Use the median when your data has outliers or is skewed. For example, housing prices and incomes are right-skewed (a few very high values), so the median better represents the typical value than the mean.
Coefficient of variation (CV) is the standard deviation divided by the mean, expressed as a percentage. It measures relative variability — useful for comparing spread between datasets with different units or scales.