Enter numbers separated by commas, spaces or new lines to compute mean, median, mode, variance (population/sample) and standard deviation — instant results and histogram.
Statistics Calculator
Enter numbers separated by commas, spaces, or new lines:
Enter numbers separated by commas, spaces, or new lines, then click Calculate.
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What is this calculator?
This tool computes basic descriptive statistics that summarize a dataset’s central tendency and spread. It’s ideal for students, teachers, data analysts, and anyone who needs quick summary statistics without writing code.
Why you might need it
Summary statistics let you quickly understand the typical value (mean/median), the most common value (mode), and how much the data varies (variance and standard deviation). They are essential for data exploration, reports, and quick checks before deeper analysis.
Some facts
Mean is sensitive to outliers; median is robust against them. Mode identifies frequently occurring values and can be multiple. Variance and standard deviation quantify spread — variance in squared units, standard deviation in original units.
Real-life examples
Use this calculator to summarize:
- Students’ exam scores to find class average and score variability.
- Daily sales numbers to check average sales and volatility.
- Sensor measurements to detect when readings deviate more than usual.
- Customer wait times to assess service consistency.
How to use (step-by-step)
1. Enter or paste your numbers (commas, spaces, or new lines are supported).
2. Choose whether to compute population or sample variance/SD if your calculator exposes this option.
3. Click Calculate. Results appear with an optional histogram for visual insight.
4. Use Clear to reset and try another dataset.
All formulas (reference)
Let the dataset be \(x_1, x_2, \dots, x_n\).
Mean (arithmetic mean) \[ \bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i \]
Median — middle value of sorted data. If \(n\) odd: median = \(x_{(k)}\) where \(k = \frac{n+1}{2}\). If \(n\) even: median = \(\frac{x_{(n/2)} + x_{(n/2 + 1)}}{2}\).
Mode — the value(s) that occur most frequently. A dataset can be unimodal, bimodal, multimodal, or have no mode.
Population variance \[ \sigma^2 = \frac{1}{n}\sum_{i=1}^{n} (x_i – \bar{x})^2 \]
Sample variance (unbiased estimator) \[ s^2 = \frac{1}{n-1}\sum_{i=1}^{n} (x_i – \bar{x})^2 \quad (n>1) \]
Population standard deviation \[ \sigma = \sqrt{\sigma^2} \]
Sample standard deviation \[ s = \sqrt{s^2} \]
Tips
• If your data contains extreme outliers, compare mean and median — large differences suggest skew or outliers.
• For small samples (n ≤ ~30) and inferential statistics, use the sample variance/SD (divide by n−1).
• If values repeat a lot (categorical-like numeric values), mode may be more informative than mean.
• Use the histogram to spot skew, multimodality, or data-entry errors.
Frequently asked questions (FAQ)
Q1: Should I use population or sample variance?
A1: Use population variance when you have measurements for the whole population you care about. Use sample variance (divide by n−1) when your dataset is a sample from a larger population and you want an unbiased estimate.
Q2: How does mode handle decimals or floating values?
A2: Mode groups exact numeric matches (e.g., 20.0 and 20 are treated the same if parsed as the same numeric value). For continuous data with many unique values, mode may be less meaningful.
Q3: My input has non-numeric tokens — what happens?
A3: The calculator ignores invalid tokens and will prompt you if no valid numbers were found. Fix typos or remove labels like ‘N/A’ before calculating.
Disclaimer
This calculator is intended for quick summary statistics and educational purposes. It does not replace rigorous statistical analysis or specialized software for advanced inferential statistics. Always validate results before using them for critical decisions.