Statistics Calculator (mean / median / mode / stddev / variance)
All 5 descriptive statistics from a list of numbers โ sample + population variants for std dev / variance.
Result
- Count (n)10
- Sum170.0000
- Mean (arithmetic average)17.000000
- Median15.500000
- Mode4 modes (multimodal)
- Min4.0000
- Max42.0000
- Range (max โ min)38.0000
- Q1 (25th percentile)8.0000
- Q3 (75th percentile)23.0000
- IQR (Q3 โ Q1)15.0000
- โ Variance + std dev โ
- Sample variance (nโ1 denom)115.333333
- Sample std deviation10.739336
- Population variance (n denom)103.800000
- Population std deviation10.188229
- Coefficient of variation (s/mean)63.17% (sample-based)
Step-by-step
- n = 10, ฮฃx = 170.0000, mean = 170.0000 / 10 = 17.0000.
- Sorted values: median = average of positions 5 and 6 = 15.5000.
- ฮฃ(x โ mean)ยฒ = 1,038.0000.
- Sample var (nโ1): 1,038.0000 / 9 = 115.3333; sample std dev = โ(115.3333) = 10.7393.
- Population var (n): 1,038.0000 / 10 = 103.8000; population std dev = โ(103.8000) = 10.1882.
How to use this calculator
- Paste your numbers โ comma-separated, space-separated, or one-per-line all work.
- Non-numeric tokens are silently skipped (so pasting from a table with labels won't break it).
- Read mean / median / mode side-by-side. For descriptive stats use SAMPLE variants by default.
About this calculator
Five descriptive statistics in one tool, plus quartiles + IQR + range + coefficient of variation. Mean is the arithmetic average ฮฃx/n. Median is the middle value (or the average of the two middle values for even n) โ robust to outliers in ways the mean is not. Mode is the most frequent value; reported as "no mode" if all values are unique. Standard deviation and variance come in TWO flavors: sample (nโ1 denominator, Bessel's correction โ the unbiased estimator when your data is a sample drawn from a larger population) and population (n denominator โ when your data IS the entire population). Use sample by default โ almost all real-world datasets are samples. The coefficient of variation (std dev / mean ร 100) is a dimensionless relative-spread measure, useful for comparing variability across datasets with different units.