Should I use sample or population standard deviation?

Use sample (n−1) when your data is a sample and you need an unbiased estimate of the population variance. Use population when your data contains the full population.

How are outliers detected?

This tool uses Tukey fences (Q1 − m×IQR, Q3 + m×IQR) to flag outliers. The multiplier m defaults to 1.5.

What percentiles can I compute?

You can compute any percentiles between 0 and 100. The default set includes 10, 25 (Q1), 50 (median), 75 (Q3), and 90.

Statistics Calculator

Descriptive statistics for a numeric dataset

Dataset (paste numbers)

Accepts comma, space, semicolon, or newline separated values. Scientific notation allowed (e.g. 1.2e3).

Or upload CSV

CSV file should contain one numeric column or multiple columns — the first numeric column will be used.

Decimal precision

How many digits after the decimal for displayed results (0–12).

Variance / SD

Sample uses n−1 denominator (unbiased). Choose population when you have the entire population.

Outlier rule

IQR multiplier for Tukey fences. Values outside [Q1 − m×IQR, Q3 + m×IQR] flagged as outliers. Set 0 to disable.

Percentiles to compute

Comma-separated percentiles 0–100. Default includes quartiles and median.

Results

Paste numbers or upload a CSV, then press Calculate.

Key definitions & interpretation

Clear, practical definitions that help you understand the numbers and choose the right measures for analysis.

Mean (average)

The arithmetic mean is the sum of values divided by the count. It is sensitive to extreme values (outliers).

Median

The median is the middle value in the sorted dataset (or the average of the two middle values when n is even). It is robust to outliers and useful for skewed distributions.

Mode

The mode is the most frequently occurring value(s) in the dataset. Datasets can have one, multiple, or no modes (if all values unique).

Variance & standard deviation

Variance measures spread (average squared deviation from the mean). Standard deviation is the square root of variance and has the same units as the data. Choose sample when you analyze a sample and want an unbiased estimate (uses n−1). Choose population when your data is the full population.

Percentiles & quartiles

Percentiles indicate the value below which a given percentage of observations fall (e.g., the 25th percentile = Q1). Quartiles divide the data into four equal parts.

IQR & Tukey fences (outlier detection)

IQR = Q3 − Q1. Tukey fences use Q1 − m×IQR and Q3 + m×IQR (m typically 1.5) to flag potential outliers. This is a robust, common rule for exploratory analysis.

Z-scores

A z-score shows how many standard deviations a value is from the mean: (x − mean) ÷ SD. It standardizes values for comparison across datasets.