Median Calculator

Median Calculator: run median calculations online. Formula, assumptions, and interpretation guide.

Descriptive statistics summarise and describe the main features of a data set using measures of central tendency (mean, median, mode), spread (range, variance, standard deviation, interquartile range), and shape (skewness, kurtosis). They are the essential first step in any data analysis — before modelling or inferring, you must understand what your data actually looks like.

Used in academic research, business analytics, quality control, public health, and sports performance, descriptive stats turn raw numbers into understandable summaries. Enter a list of values and instantly see the full statistical profile.

Enter your data values separated by commas or spaces (e.g. 12, 15, 18, 14, 20).
The calculator automatically computes count, sum, mean, median, mode, range, variance, and standard deviation.
Check the min and max values to spot potential data entry errors or outliers.
Compare the mean and median — a large difference suggests skewed data or outliers pulling the average.
Use the interquartile range (IQR) to understand where the middle 50% of values sit.

Core descriptive statistics formulas

Mean (x̄) = Σx / n — sum of all values divided by count

Variance (s²) = Σ(x − x̄)² / (n − 1) — average squared deviation (sample)

Standard deviation (s) = √variance — typical spread around the mean

IQR = Q3 − Q1 — range of the middle 50% of data

Outlier bounds: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are flagged as outliers (Tukey method)

Reading your descriptive statistics results

What the numbers tell you

A low standard deviation means values cluster tightly around the mean; a high value means wide spread. If median is much lower than mean, the distribution is right-skewed (a few large values pulling the average up) — common in income data. Mode is the most frequent value; in a truly normal distribution, mean, median, and mode are equal.

Statistics tips and best practices

Always look at the distribution shape before interpreting the mean — the mean is misleading for skewed data.
Use median and IQR instead of mean and standard deviation when data contains outliers.
Check your sample size: statistics from very small samples (n < 10) are unreliable.
Sort the data visually before entry to spot gaps, duplicates, or data entry errors.

The US household income distribution is strongly right-skewed: the mean is approximately $105,000 but the median is about $74,000 — the difference reflects a relatively small number of very high earners.
In a perfectly normal distribution, 68% of values fall within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 (the empirical rule).
The IQR is used by the US CDC and WHO for reporting health data distributions to reduce the influence of extreme values.

Common mistakes to avoid

Confusing population variance (÷ n) with sample variance (÷ n−1) — almost all real-world analyses use the sample formula.
Reporting only the mean without the standard deviation — this hides whether data is tightly clustered or wildly spread.
Ignoring outliers instead of investigating them — they may represent data errors or genuinely important extreme cases.

Descriptive statistics are summary tools. They do not establish causation, statistical significance, or predictive validity. For research or business decisions, consult a qualified statistician.