Math

Statistics Calculator

Enter numbers to get mean, median, mode, standard deviation, quartiles, and more.

Data Set (commas, spaces, or new lines)

0 values

Formulas

Mean (x̄)

Σxᵢ / n

Sum of all values divided by count

Sample Std Dev (s)

√[Σ(xᵢ−x̄)² / (n−1)]

Spread for a sample; divides by n−1

Pop. Std Dev (σ)

√[Σ(xᵢ−μ)² / n]

Spread for full population; divides by n

Median of lower half (excl. median)

25th percentile

Median of upper half (excl. median)

75th percentile

IQR

Q3 − Q1

Middle 50% spread; robust to outliers

Sample (s, s²)

Data is a subset of a larger group. Uses n−1 (Bessel's correction) to reduce underestimation bias.

Population (σ, σ²)

Data represents every member of the group. Uses n exactly.

When n > 30, the difference is negligible. Default to sample std dev in most real-world cases.

Mean vs Median: If they differ greatly, data is skewed or has outliers. Median is more robust.

Std Dev: ~68% of normally distributed data falls within 1σ of the mean; ~95% within 2σ.

Outlier rule: Values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are typically flagged as outliers.