Statistics Batch Calculator
Mean, median, mode, std deviation, variance, quartiles for any list of numbers. Histogram + box plot visualizations.
Math
Statistics Batch Calculator
Generated on April 25, 2026
10 numbers parsed
Histogram (frequency distribution)
Box plot (5-number summary)
Step-by-step calculation
Formula
Mean = Σx/n. Variance = Σ(x − mean)²/n. Std dev = √variance. Median = middle value (or mean of two middle values when n is even). Q₁/Q₃ = 25th/75th percentiles.
- 1n = 10 values, sorted: [12, 15, 18, 20, 22, 22, 25, 28, 30, 35]
- 2Sum = 227. Mean = 227 / 10 = 22.7.
- 3Median (middle pair averaged) = 22.
- 4Mode = 22 (each appears 2 times).
- 5Variance σ² = mean of squared deviations from the mean = 44.21.
- 6Standard deviation σ = √variance = 6.649 — typical distance from the mean.
- 7Q₁ = 18.5, Q₃ = 27.25, IQR = Q₃ − Q₁ = 8.75 (middle-50% spread).
- 8Note: this calculator uses POPULATION variance (divide by n). Sample variance (divide by n−1) would give 49.122.
?What is the Statistics Batch Calculator?
The Statistics Batch Calculator computes every common descriptive statistic — count, sum, mean, median, mode, range, variance, standard deviation, Q1/Q3 quartiles, and IQR — for any list of numbers you paste in (separated by commas, spaces, or new lines). Visualized as both a histogram (Sturges' rule for bin count) showing the frequency distribution with mean and median markers, and a box plot showing the 5-number summary (min, Q1, median, Q3, max) with mean as a diamond marker. Used for school stats homework, exploratory data analysis, A/B test analysis, quality control, and any decision based on summary statistics of a small-to-medium dataset.
The Formula
This calculator uses POPULATION variance (divide by n) — the right choice when your numbers ARE the entire population, not a sample drawn from a larger population. For SAMPLE variance (when you have a subset of a larger group and want to estimate the population's variance), divide by (n−1) instead — the calculator shows that value too in the steps. The 'mode' is the most-frequent value; if no value repeats, there is no mode (the calculator says so). If multiple values tie for most-frequent, all are reported.
Practical Examples
Class test scores: input the scores of 30 students to get class average (mean), middle score (median), most-common score (mode), and how spread-out the scores are (std dev).
Revenue analysis: paste daily sales for a month → mean, median, range, and IQR show typical performance and outliers.
Survey data: median is more robust than mean when there are extreme responses (outliers).
Quality control: a batch of 100 measurements with low std dev means consistent process; high std dev means investigate.
Box plot quickly shows whether data is symmetric (mean ≈ median) or skewed (large gap between mean and median).
Frequently Asked Questions
Popular Conversions
Jump to a ready-made conversion — useful for quick reference and sharing:
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