Compute Descriptive Statistics Step by Step
AI models frequently estimate or round statistics. This tool computes exact values using the correct population and sample formulas, with every step shown.
Paste from Excel or Sheets. Supports value:frequency shorthand, e.g. 10:3 means the value 10 appears 3 times.
What This Statistics Calculator Computes
This tool calculates descriptive statistics. You can enter a list of numbers and select whether it's a sample — which is a subset used to estimate a larger group, and is calculated by dividing by n−1 — or a population, where you have every member and divide by n. Either way, you'll get all the common summary statistics.
Key Measures
- Mean — the arithmetic average: sum of values divided by the count.
- Median — the middle value after sorting; for an even count, the average of the two middle values.
- Mode — the most frequently occurring value (all modes are listed).
- Standard Deviation — how spread out values are around the mean. Sample uses n−1 (Bessel's correction); population uses n.
- Variance — the square of the standard deviation.
- Quartiles & IQR — Q1, Q2 (median), Q3 and the interquartile range (Tukey method).
- Z-Scores — how many standard deviations each value sits from the mean, with outliers flagged.
- Standard Error — the sample standard deviation divided by the square root of the count.
Why Use This Tool Instead of AI?
A stats calculator applies the exact formula each time and shows how it works. Everything runs locally in your browser, so your data never leaves your device. Unlike AI models, it never rounds early or mixes up the sample and population formulas — you can hand in the working or check it against your own notes.
How to Use
- Paste or type your numbers separated by commas, spaces, or line breaks.
- Choose Sample or Population depending on your data set.
- Click Calculate to see all summary statistics plus a step-by-step breakdown.
- Use the example chips to quickly test common datasets.
Frequently Asked Questions
What is the difference between sample and population standard deviation?
A population includes every member of the group, so you divide by n. A sample is a subset used to estimate a larger group, so you divide by n−1 (Bessel's correction) to avoid underestimating the spread.
How is the median calculated for an even number of values?
After sorting, the median is the average of the two middle values. For example, in 1, 2, 3, 4 the median is (2 + 3) ÷ 2 = 2.5.
Can I paste a frequency table?
Yes. Use the value:frequency format. For instance, 10:3,20,30:2 expands to 10, 10, 10, 20, 30, 30 before calculation.
How are the quartiles calculated?
This tool uses the Tukey method: the median splits the sorted data in half, and Q1 and Q3 are the medians of the lower and upper halves. Q3 minus Q1 gives the interquartile range (IQR).
Is my data private?
Yes. Every calculation runs entirely in your browser. No data is sent to any server, uploaded, or stored.
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