Dataset Analyzer: Descriptive Statistics from Any Pasted Dataset
Paste your numbers, get your statistics instantly. This dataset analyzer computes the full set of descriptive statistics — mean, median, mode, standard deviation (population and sample), variance, range, quartiles, interquartile range, and outliers — without uploading your data anywhere. Paste a column of numbers, a CSV row, or a space-separated list and the results appear immediately in your browser.
Quartiles (Q1, Q3) are computed using linear interpolation at the 25th and 75th percentiles of the sorted dataset. The mode returns all values that appear most frequently (there may be multiple modes, or none if all values are unique).
Mean vs. Median — When Each Is More Useful
The choice between mean and median is fundamentally about how outliers should affect your summary. If your dataset has no extreme values and is roughly symmetric, mean and median will be close — use mean because it is more statistically tractable (easier to use in further calculations). If your data is skewed — long tail of high values (income, house prices, response times) or low values — median is the better measure of the 'typical' value. A company reporting 'average salary' when a few executives earn 10× the typical employee is using mean to mislead; median would tell a different story. When in doubt, report both.
Standard Deviation Explained Simply
Standard deviation tells you how tightly clustered your data is around the mean. A class where every student scored between 70 and 80 has a low standard deviation (~3). A class where scores ranged from 20 to 100 has a high standard deviation (~25). The practical rule for normally distributed data: about 68% of values are within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3. This is why 'two sigma' is a common threshold for quality control — a measurement more than 2 standard deviations from the expected value is unusual enough to investigate.
The Five-Number Summary and Box Plots
The five-number summary — Minimum, Q1, Median, Q3, Maximum — describes the distribution of a dataset without assuming any particular shape. It is the basis for a box plot (also called a box-and-whisker plot): the box spans from Q1 to Q3 (the IQR), a line marks the median, and whiskers extend to the most extreme non-outlier values. Data points beyond the whiskers are plotted individually as outlier dots. Box plots make it easy to compare distributions side by side — you can see center, spread, skew, and outliers at a glance.
Identifying Outliers with the IQR Method
The Tukey fence method (named after statistician John Tukey) is the most widely used outlier detection rule: compute IQR = Q3 − Q1, then flag any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR as an outlier. The 1.5 multiplier is a convention — some analysts use 3.0 for 'extreme' outliers. Before removing outliers, always investigate: they may be data entry errors (a weight entered as 750 kg instead of 75 kg), measurement failures, or genuine extreme values that are the most interesting part of your data. Removing them without understanding them is a common analysis mistake.
When to Use Mean vs. Median
- Symmetric data, no extreme outliers → mean
- Skewed data (income, prices, time-to-event) → median
- Categorical / ordinal data → mode (not mean or median)
- Both are useful → report both and note the skew
- Normal distribution assumed → mean is required for further inference
- Reporting 'typical' user experience (load times, session length) → median
The Five-Number Summary Quick Guide
- Min — smallest value in the dataset
- Q1 (25th percentile) — 25% of values are below this
- Median (Q2, 50th percentile) — half above, half below
- Q3 (75th percentile) — 75% of values are below this
- Max — largest value in the dataset
- IQR = Q3 − Q1 — the spread of the middle half
Frequently Asked Questions
What is the difference between mean and median?
The mean (arithmetic average) is the sum of all values divided by the count. The median is the middle value when the dataset is sorted — exactly half the values are above it and half below. They are equal in a perfectly symmetric distribution but diverge when data is skewed. The mean is pulled toward extreme values (outliers); the median is not. A dataset of [1, 2, 3, 4, 100] has a mean of 22 but a median of 3.
When should I use median instead of mean?
Use median whenever your data is skewed or contains outliers that don't represent the typical case. Income and house price data are classic examples: a neighborhood's mean income can be inflated by a handful of very high earners, while the median reflects what a typical resident actually earns. Other cases where median is more informative: response times in web performance (a slow 99th percentile outlier skews the mean), dataset sizes, and test scores with extreme failures.
What is standard deviation?
Standard deviation measures how spread out values are from the mean. A low standard deviation means most values cluster close to the mean; a high standard deviation means they are spread widely. In a normal (bell-curve) distribution, 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three (the empirical rule). Standard deviation is in the same units as the original data, making it more interpretable than variance.
What is an outlier in statistics?
An outlier is a data point that lies far from the rest of the dataset. The most common detection method is the IQR fence rule: any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is classified as an outlier. For example, if Q1 = 25, Q3 = 75, IQR = 50, then the fences are 25 − 75 = −50 and 75 + 75 = 150 — any value outside [−50, 150] is an outlier. Outliers may represent data entry errors, measurement failures, or genuinely extreme but valid observations.
What is the difference between variance and standard deviation?
Variance is the average of squared deviations from the mean: Σ(x − μ)² / n. Standard deviation is the square root of variance. Squaring the deviations makes variance always positive and amplifies large deviations, but the result is in squared units (e.g., square meters for area data, square dollars for financial data) — which is hard to interpret directly. Taking the square root gives standard deviation back in the original units, making it the more commonly reported measure of spread.
What is the difference between population and sample standard deviation?
When your dataset is the entire population (every member of the group you care about), divide by n. When your dataset is a sample drawn from a larger population and you are estimating the population's spread, divide by n − 1. Dividing by n − 1 (Bessel's correction) corrects for the fact that a sample tends to underestimate the true population spread. In practice, for large datasets the difference is negligible, but it matters for small samples (n < 30).
What is the interquartile range?
The interquartile range (IQR) is Q3 − Q1 — the spread of the middle 50% of your data. Because it ignores the top 25% and bottom 25% of values, it is robust against outliers in a way that range (max − min) is not. The IQR is the key statistic behind box plots: the box spans from Q1 to Q3, the line inside is the median, and the 'whiskers' extend to the IQR fence values (Q1 − 1.5×IQR and Q3 + 1.5×IQR).