What is the difference between population and sample variance?

Population variance divides by n (the total count). Sample variance divides by n−1 (Bessel's correction) to account for the fact that a sample underestimates the true population variability.

How is the median calculated?

Sort the data. If the count is odd, the median is the middle value. If even, it is the average of the two middle values.

What if there is no mode?

If no value repeats, the dataset has no mode. If multiple values tie for most frequent, all are modes (multimodal). This calculator shows the first mode found.

What is the IQR used for?

The interquartile range (Q3 − Q1) measures the spread of the middle 50% of data. It is used to detect outliers: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are potential outliers.

How many numbers can I enter?

You can enter as many numbers as needed. Separate them with commas. Spaces and empty entries are ignored automatically.

Math

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Statistics Calculator

Calculate mean, median, mode, range, variance, standard deviation, quartiles, IQR, and more from a list of numbers.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

The statistics calculator computes a full set of descriptive statistics from a list of comma-separated numbers. It covers central tendency (mean, median, mode), dispersion (range, variance, standard deviation), position (Q1, Q3, IQR), and summary values (min, max, count, sum).

Numbers (comma-separated)

What is Statistics Calculator?

How to use it

1️⃣ Enter your numbers separated by commas in the text area.
2️⃣ Numbers can include decimals and negatives.
3️⃣ Click Calculate to compute all statistics instantly.
4️⃣ Both population and sample variance/standard deviation are shown.
5️⃣ Quartiles use the inclusive method (Q1 = median of lower half).

Formula

Mean = Σx/n. Median = middle value (sorted). Mode = most frequent value. Population variance σ² = Σ(x−μ)²/n. Sample variance s² = Σ(x−x̄)²/(n−1). IQR = Q3 − Q1.

💡 See it in action — a real example

Data: 2, 4, 4, 4, 5, 5, 7, 9. Mean = 5, Median = 4.5, Mode = 4, Range = 7, Population SD ≈ 1.77, Sample SD ≈ 2.0.

❓ Common questions

What is the difference between population and sample variance?: Population variance divides by n (the total count). Sample variance divides by n−1 (Bessel's correction) to account for the fact that a sample underestimates the true population variability.
How is the median calculated?: Sort the data. If the count is odd, the median is the middle value. If even, it is the average of the two middle values.
What if there is no mode?: If no value repeats, the dataset has no mode. If multiple values tie for most frequent, all are modes (multimodal). This calculator shows the first mode found.
What is the IQR used for?: The interquartile range (Q3 − Q1) measures the spread of the middle 50% of data. It is used to detect outliers: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are potential outliers.
How many numbers can I enter?: You can enter as many numbers as needed. Separate them with commas. Spaces and empty entries are ignored automatically.

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