liminfoStatistics Calculator
Free web tool: Statistics Calculator
About Statistics Calculator
The Statistics Calculator is a comprehensive browser-based tool that computes 17 descriptive statistics from any numeric dataset. Simply enter your numbers separated by commas or spaces, click Calculate, and instantly receive: count, sum, minimum, maximum, range, mean (arithmetic average), median, mode, Q1, Q3, interquartile range (IQR), population variance, sample variance, population standard deviation, sample standard deviation, skewness, and excess kurtosis. All results can be copied to the clipboard as formatted text.
This tool is widely used by students completing statistics homework, researchers performing exploratory data analysis, teachers verifying textbook answers, data analysts doing quick sanity checks, and quality control engineers computing process capability metrics. It handles both small datasets (5 numbers) and larger sets equally well, since all computation happens client-side in the browser using optimized JavaScript functions.
The calculator implements statistically correct algorithms: median correctly handles both odd and even dataset sizes, mode returns empty when all values appear exactly once (no mode), sample variance divides by (n-1) using Bessel's correction while population variance divides by n, skewness uses the standard adjusted Fisher-Pearson formula accounting for sample size bias, and excess kurtosis subtracts 3 from the fourth standardized moment to give a value of 0 for a normal distribution.
Key Features
- Computes 17 descriptive statistics in a single click: count, sum, min, max, range, mean, median, mode, Q1, Q3, IQR, population/sample variance, population/sample std dev, skewness, and excess kurtosis
- Accepts comma-separated or space-separated numeric input — mixed separators work too
- Correct statistical implementations: Bessel's correction for sample variance, adjusted Fisher-Pearson skewness, excess kurtosis centered at 0 for normal distributions
- Mode detection returns "None" when all values are unique, and handles multimodal datasets
- Quartile computation using the inclusive median method (lower/upper halves of sorted data)
- Results displayed in a two-column grid for easy side-by-side comparison
- Copy all results to clipboard as plain text (label: value) with a single button click
- 100% client-side — no data ever leaves your browser, works with sensitive research data
Frequently Asked Questions
What statistics does this calculator compute?
The calculator outputs 17 values: Count (n), Sum, Min, Max, Range, Mean (arithmetic average), Median, Mode, Q1 (1st Quartile), Q3 (3rd Quartile), IQR (Interquartile Range = Q3 - Q1), Population Variance, Sample Variance, Population Standard Deviation, Sample Standard Deviation, Skewness (adjusted Fisher-Pearson), and Excess Kurtosis (fourth standardized moment minus 3).
What is the difference between population variance and sample variance?
Population variance divides the sum of squared deviations from the mean by n (the total number of values), and is used when your dataset represents the entire population. Sample variance divides by (n-1) — known as Bessel's correction — and is used when your dataset is a sample from a larger population. Sample variance is an unbiased estimator of population variance, which is why the (n-1) denominator is used for inferential statistics.
How is the median calculated for an even number of data points?
For an even number of values, the median is the arithmetic mean of the two middle values after sorting. For example, for the dataset [10, 20, 30, 40], the two middle values are 20 and 30, so the median is (20+30)/2 = 25. For an odd count, the median is simply the middle value of the sorted dataset.
What does it mean when mode shows "None"?
Mode is "None" when every value in the dataset appears exactly once (no value is repeated more than any other). In this case, no single value is "most frequent," so by statistical convention there is no mode. When multiple values tie for the highest frequency, the calculator lists all of them as the mode (multimodal dataset).
What is skewness and how should I interpret it?
Skewness measures the asymmetry of a distribution. A value near 0 indicates a roughly symmetric distribution. Positive skewness (right skew) means the tail extends further to the right — the mean is typically greater than the median. Negative skewness (left skew) means the tail extends further to the left. Values between -0.5 and 0.5 are generally considered approximately symmetric; beyond ±1 indicates strong skewness.
What is excess kurtosis and what does a value of 0 mean?
Excess kurtosis measures the "tailedness" of a distribution relative to a normal distribution. A normal distribution has excess kurtosis of 0 (this is why 3 is subtracted from the raw kurtosis). Positive excess kurtosis (leptokurtic) means heavier tails than normal — more extreme outliers. Negative excess kurtosis (platykurtic) means lighter tails — fewer outliers. The calculator uses the corrected formula accounting for small sample bias.
How do I enter data into the calculator?
Enter your numbers in the text area separated by commas (10, 20, 30), spaces (10 20 30), or a mix of both. Non-numeric values are automatically filtered out. Press the Calculate button (or the 계산 button) to see all results. The default sample data "10, 20, 30, 40, 50, 20, 30, 30, 60, 70" is pre-filled so you can immediately see what the output looks like.
What is the IQR (Interquartile Range) and why is it useful?
The Interquartile Range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1): IQR = Q3 - Q1. It represents the range of the middle 50% of the data and is a robust measure of spread that is not affected by extreme outliers. A common rule for outlier detection is: values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered potential outliers (the Tukey fence method).