Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, and more from a list of numbers.

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Statistics Calculator
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How to use Statistics Calculator

Descriptive statistics summarize a dataset with a few key numbers — measures of center, spread, and distribution. This calculator computes the full suite of descriptive statistics from any list of numbers you enter. How to enter data: Type numbers separated by commas, spaces, or new lines. For example: 23, 45, 12, 67, 34. Paste directly from a spreadsheet column — comma or newline-separated values are both accepted. Up to 10,000 values are supported. Measures of center (central tendency): Mean (average) — sum of all values divided by count. Sensitive to outliers. Median — the middle value when sorted. Robust to outliers. Mode — the most frequently occurring value(s). Useful for categorical-like numeric data. Geometric mean — useful for growth rates and financial returns. Harmonic mean — useful for rates and ratios. Measures of spread (dispersion): Range — maximum minus minimum. Simplest measure of spread. Variance — average of squared deviations from the mean. Population and sample variance both shown. Standard deviation — square root of variance. Same units as the data. Shows typical distance from the mean. Coefficient of variation — standard deviation as a percentage of mean. Compares spread across datasets with different scales. Interquartile range (IQR) — difference between 75th and 25th percentiles. Robust to outliers. Percentiles and quartiles: Q1 (25th), median (50th), Q3 (75th) percentile. Custom percentile input. Distribution shape: Skewness — positive skew means tail on right (outliers above mean), negative means tail on left. Kurtosis — measures tail heaviness relative to a normal distribution.

Frequently Asked Questions

What is the difference between population and sample standard deviation?

Population standard deviation (sigma) divides the sum of squared deviations by N (total count) — used when you have data for an entire population. Sample standard deviation (s) divides by N-1 (Bessel's correction) — used when your data is a sample from a larger population. Sample SD is always slightly larger. In practice, use sample SD for data analysis unless you are certain you have the complete population.

When should I use median instead of mean?

Use median when the data contains outliers or is skewed. The mean is pulled toward extreme values — a dataset of incomes where one billionaire earns Rs 100 crore makes the mean misleading for the typical income. The median is resistant to outliers. When mean and median differ significantly, the data is skewed and the median better represents the "typical" value.

What does standard deviation tell me about my data?

Standard deviation measures how spread out values are around the mean. A low SD means values cluster close to the mean; a high SD means they are spread widely. For a normal distribution: approximately 68% of values fall within 1 SD of the mean, 95% within 2 SD, 99.7% within 3 SD. This lets you identify outliers (values more than 2-3 SD from the mean) and understand data variability.

What is interquartile range and when is it useful?

IQR is the difference between the 75th percentile (Q3) and 25th percentile (Q1). It represents the spread of the middle 50% of data, making it robust to outliers. IQR is used for box-and-whisker plots and outlier detection — values more than 1.5 x IQR below Q1 or above Q3 are commonly flagged as outliers.

What does skewness indicate about my dataset?

Skewness measures asymmetry of the distribution. A skewness near 0 indicates a roughly symmetric distribution. Positive skewness (right skew) means a long tail on the right — most values are lower but some very large values pull the tail. Income distributions are typically right-skewed. Negative skewness (left skew) means a long tail on the left — most values are high with some very low outliers.

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