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Statistics Calculator

Calculate mean, median, mode, range, variance, and standard deviation for any set of numbers. Instant results with full statistical breakdown.

Separate numbers with commas, spaces, or new lines.

9 numbers
47132794156
Mean (Average)7.444444Sum ÷ Count
Median7Middle value
Mode4, 7Most frequent values
Count9Total numbers
Sum67Total of all values
Range13Max − Min
Min2Smallest value
Max15Largest value
Std Deviation (σ)4.030746Population std dev
Std Deviation (s)4.275252Sample std dev
Variance (σ²)16.246914Population variance
Variance (s²)18.277778Sample variance
Quartiles
Q14
Median (Q2)7
Q39
IQR5

How to Use This Tool

  1. Type or paste your numbers into the text area, separating them with commas, spaces, semicolons, or new lines.
  2. Review the parsed number chips to confirm every value was read correctly.
  3. Read the results grid for mean, median, mode, count, sum, range, min, max, standard deviation, and variance.
  4. Check both standard deviation (σ) and variance (σ²) for the full population, or the sample versions (s, s²) if your data is a sample.
  5. Review the quartiles (Q1, Median/Q2, Q3) and IQR for the spread of the middle 50% of your data.
  6. Use Sort ↑ or Sort ↓ to reorder the numbers, or Clear to start over.

Formula & How It Works

Mean

x̄ = (Σx) / n

Add up all the values and divide by how many values there are.

Population Variance & Std Deviation

σ² = Σ(x − x̄)² / n, σ = √σ²

Averages the squared distance of every value from the mean, dividing by n; used when your data is the entire population.

Sample Variance & Std Deviation

s² = Σ(x − x̄)² / (n − 1), s = √s²

Same as population variance but divides by n − 1 instead of n, which corrects for bias when your data is only a sample.

Quartiles & IQR

IQR = Q3 − Q1

Q1 and Q3 are the 25th and 75th percentiles of the sorted data (using linear interpolation); IQR measures the spread of the middle 50% of values.

Practical Examples & Common Use Cases

Example: Mean of 4, 7, 13, 2, 9

Sum = 4 + 7 + 13 + 2 + 9 = 35. Mean = 35 / 5 = 7.

Example: Median of 4, 7, 13, 2, 9

Sorted: 2, 4, 7, 9, 13. With 5 values, the median is the middle one: 7.

Example: Population Std Dev of 2, 4, 4, 4, 5, 5, 7, 9

Mean = 5. Squared deviations sum to 32. Population variance = 32 / 8 = 4, so population std dev σ = √4 = 2. Sample variance would instead divide by 7, giving 32/7 ≈ 4.57, with sample std dev s ≈ 2.14.

Frequently Asked Questions

The mean is the arithmetic average (sum ÷ count). The median is the middle value when data is sorted. Median is less affected by extreme outliers.

If all values appear the same number of times, there is no mode. This calculator will show "None" in that case.

Use population standard deviation (σ) when your dataset represents the entire population. Use sample standard deviation (s) when your data is a sample of a larger population.

The Interquartile Range (IQR = Q3 − Q1) measures the spread of the middle 50% of data. It's commonly used to detect outliers: values beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR are considered outliers.

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