Statistics Calculator
Paste numbers for the count, sum, mean, median, mode, range, quartiles, IQR, variance and standard deviation — with a histogram, a box plot and the outliers.
The shape of it
The box spans the middle half of the values, the line inside it is the median, and the whiskers reach the furthest value within 1.5 interquartile ranges. Anything past that is drawn as a dot.
Outliers: None — every value is within 1.5 × IQR of the quartiles.
Normality (Shapiro–Wilk): W = 0.965338, p = 0.863004 — no evidence against a normal distribution at the 0.05 level — which does not prove it is one
Frequency tableDescriptive statistics in one paste
Enter your numbers separated by commas, spaces, or new lines and the table updates live with every common summary statistic: count, sum, mean, median, mode, min, max, range, the first and third quartiles (Q1/Q3), the interquartile range (IQR), and variance and standard deviation in both their population and sample forms, the standard error of the mean, skewness (population and sample), the mid range, sum of squares, mean absolute deviation and root mean square. The last two rows are the sum of the squared values themselves (Σx²) and the geometric mean, which shows a dash when a value is negative. Under the box plot a frequency table counts how often each value occurs. Non-numeric tokens are ignored, so a column copied straight out of a spreadsheet or a log file works as it is. Copy the whole summary as plain text with one click. The “Separator”, “Decimal mark” and “Thousands separator” selects say how your numbers are written — comma-separated CSV, tab-separated TSV or semicolons; a decimal comma; a comma, a point or a space between the thousands — and the page remembers them on this device until you press “Forget saved settings”; a choice that cannot be read one way, such as a comma that is both the decimal mark and the separator, is refused with the reason. With a separator chosen, “Statistics per column (first row is the column names)” reads each column on its own: a “Per column” table gives each column's count, mean, median, sample standard deviation, minimum and maximum, and the “Column” select chooses which column the full table, the charts and the frequency table describe — the columns are not pooled into one list.
And the shape, which no table shows
Under the numbers the page draws the same data twice. The histogram shows how many values fall where, with a slider for how many bars — a second hump, a long tail or a gap in the middle is visible there and nowhere in the table. The box plot draws the middle half of the values as a box with the median as a line through it, whiskers out to the furthest value within 1.5 interquartile ranges, and a dot for anything beyond that. A median sitting hard against one side of the box is skew; the table's skewness rows put a number on it, and the picture shows where the lean comes from. Outliers are also listed by value underneath, and when there are none the page says so. The “Outlier rule” select under the list chooses what counts: Tukey's fences, as the box plot draws them (the default), the wider far-out fence, or a distance from the mean in sample standard deviations. Under it, “Normality (Shapiro–Wilk)” gives W and p and reads them at the conventional significance level — no evidence against a normal distribution, which does not prove the data is normal, or unlikely to be from a normal distribution — and says so when the list has too few or too many values for the test.
How each value is calculated
The mean is the sum divided by the count. The median is the middle value once sorted, or the average of the two middle values when the count is even. The mode lists every value that appears most often, and shows a dash when every number is unique. The quartiles split the sorted data into four parts: Q1 is the median of the lower half and Q3 the median of the upper half, computed with the median-of-halves method (for an odd count the overall median sits in neither half), and the interquartile range is Q3 − Q1. Variance and standard deviation are given both ways — the population formula for when your numbers are the entire set, and the sample formula with Bessel’s correction for when they are a sample drawn from something larger.
Frequently asked questions
Do you use population or sample standard deviation?
Both, on their own rows. Use the population figures when your numbers are the whole set you care about, and the sample figures — which divide by one less than the count, known as Bessel’s correction — when they are a sample standing in for something larger. The sample rows show a dash for a single value, because a sample of one has no spread to estimate.
How do I spot an outlier?
The box plot draws one as a dot beyond the whiskers, and every one is listed by value underneath. By default the test is the standard one: more than 1.5 interquartile ranges below Q1 or above Q3. The “Outlier rule” select changes which values are listed — the far-out fence, or a distance from the mean in sample standard deviations — while the box plot keeps the standard fences. When nothing qualifies the page says so explicitly.
What do the bars in the histogram mean?
The range from the smallest value to the largest is cut into equal-width bars, and each bar is how many values landed in it. The slider changes how many bars there are — fewer for the overall shape, more to see where the values actually cluster. A value on a boundary counts in the bar it opens, so nothing is counted twice.
Can I paste a column from a spreadsheet?
Yes. Line breaks, commas and spaces all separate values, and anything that is not a number is skipped, so a pasted column — headers, blank cells and all — still gives clean results, and a currency sign on either end of a value ($12.50, 10.00€) is read off it. A thousands separator is not guessed at: 1,718 splits at the comma into 1 and 718, and the page names each figure written that way — unless you set “Thousands separator” to Comma and “Separator” to Tab or Semicolon, when it is read as one value.
What do skewness and the frequency table add?
Skewness is one number for which way the data leans: positive for a long tail to the right, negative for one to the left, near zero for a symmetric set. It is given in the population form and in the sample form with the usual small-sample adjustment, and shows a dash where its formula has no value — every value equal, or too few values for the sample form. The frequency table under the box plot lists each distinct value with how many times it occurs and its share of the total, lowest value first; for a very long list it shows the lowest and says how many it left out.
Does it give kurtosis and the coefficient of variation, and can I round the figures?
Yes. “Kurtosis (population, β₂)” is Σ(x − μ)⁴ / nσ⁴, and beside it the excess kurtosis in the sample form — the figure KURT returns in Excel and Sheets. The coefficient of variation divides the sample standard deviation by the size of the mean, and the relative standard deviation is the same thing as a percentage. Each shows a dash where its formula has no value: every value equal, a mean of 0, or too few values for the sample form. “Decimal places” rounds every figure — the table, the frequency percentages, the outliers and the histogram's bar labels — and the copied and downloaded text with it. The table also gives the sum of the squared values (Σx²) and the geometric mean.
Can it test whether my data is normally distributed?
Yes. Under the outliers, “Normality (Shapiro–Wilk)” gives the W statistic and its p-value and reads them at the conventional significance level: either no evidence against a normal distribution — which does not prove the data is normal — or unlikely to be from one. It follows Royston's method, the one R and SciPy use, and says so when the list is too short or too long for the test.
Can it give statistics for each column?
Yes. Choose a “Separator” — Comma (CSV), Tab (TSV) or Semicolon — and tick “Statistics per column (first row is the column names)”. A “Per column” table then gives each column's count, mean, median, sample standard deviation, minimum and maximum, and the “Column” select chooses which column the full table, the histogram, the box plot and the frequency table describe. A column with no name is called by its place, and a repeated name gets a number after it. The automatic separator cannot do this, because it splits at every space.