Smart Unit ConvertersSmart Unit Converters

Statistics Batch Calculator

Mean, median, mode, std deviation, variance, quartiles for any list of numbers. Histogram + box plot visualizations.

10 numbers parsed

Summary statistics
Count
10
Sum
227
Mean
22.7
Median
22
Mode
22
Std Dev (σ)
6.649
Variance (σ²)
44.21
Range
23
Min
12
Q₁ (25%)
18.5
Q₃ (75%)
27.25
Max
35

Histogram (frequency distribution)

1223.535μM
μ = mean · M = median · 5 bins (Sturges' rule)

Box plot (5-number summary)

12Q₁ 18.5M 22Q₃ 27.2535
Box = middle 50% (IQR = 8.75) · green = median · pink ◇ = mean

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.

  1. 1n = 10 values, sorted: [12, 15, 18, 20, 22, 22, 25, 28, 30, 35]
  2. 2Sum = 227. Mean = 227 / 10 = 22.7.
  3. 3Median (middle pair averaged) = 22.
  4. 4Mode = 22 (each appears 2 times).
  5. 5Variance σ² = mean of squared deviations from the mean = 44.21.
  6. 6Standard deviation σ = √variance = 6.649 — typical distance from the mean.
  7. 7Q₁ = 18.5, Q₃ = 27.25, IQR = Q₃ − Q₁ = 8.75 (middle-50% spread).
  8. 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

Mean = Σx/n. Median = middle value. Mode = most frequent. Variance σ² = Σ(x − mean)²/n (population) or /(n−1) (sample). Std dev σ = √variance. Q1/Q3 = 25th/75th percentiles.

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

1

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).

2

Revenue analysis: paste daily sales for a month → mean, median, range, and IQR show typical performance and outliers.

3

Survey data: median is more robust than mean when there are extreme responses (outliers).

4

Quality control: a batch of 100 measurements with low std dev means consistent process; high std dev means investigate.

5

Box plot quickly shows whether data is symmetric (mean ≈ median) or skewed (large gap between mean and median).

Frequently Asked Questions

Mean (average) sums everything and divides by count — sensitive to outliers. Median is the middle value when sorted — robust to outliers. For 10 salaries [40k, 45k, 50k, 55k, 60k, 65k, 70k, 75k, 80k, 1M], mean = 154k (skewed by the outlier), median = 62.5k (the typical salary).

Popular Conversions

Jump to a ready-made conversion — useful for quick reference and sharing: