Statistics Calculator
One paste, every summary statistic: count, sum, min, max, range, mean, median, mode, sample and population standard deviation and variance, quartiles, IQR, and geometric mean. Commas, spaces, or new lines all work as separators.
Sorted data & steps
What each statistic tells you
The mean is the balance point of the data and moves with outliers; the median is the middle value and resists them — when the two differ a lot, the data is skewed. The mode is the most frequent value, range the full spread, and the IQR (Q3 − Q1) the spread of the middle half, which is what box plots draw. Standard deviation summarizes typical distance from the mean, and the geometric mean (nth root of the product) is the right average for growth rates and ratios — it only exists when every value is positive.
How it’s calculated
Mean = Σx ÷ n; median = middle of the sorted list (average of the two middles when n is even). Quartiles use the median-of-halves method: Q1 is the median of the lower half and Q3 of the upper half, excluding the overall median when n is odd. Variance = Σ(x − x̄)² ÷ n (population) or ÷ (n − 1) (sample); SD = √variance. Geometric mean = exp(Σln x ÷ n), positive data only.
Results update as you type and are for education, not professional advice — double-check any number that matters.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9: n = 8, sum = 40, mean = 5, median = (4 + 5) ÷ 2 = 4.5, mode = 4 (appears 3 times), range = 9 − 2 = 7. Population SD = 2 (variance 4); sample SD = 2.1381 (variance 4.5714). The lower half 2, 4, 4, 4 gives Q1 = 4; the upper half 5, 5, 7, 9 gives Q3 = 6, so IQR = 2. Geometric mean = 2016001/8 ≈ 4.6032.
Common mistakes
- Reporting the mean alone on skewed data — one big outlier can drag it far from a typical value.
- Forgetting there can be two modes (or none) — this tool lists every tied value.
- Comparing quartiles from different tools without checking the method — interpolation methods give slightly different Q1/Q3.
Where it is used
- Summarizing survey results, test scores, or lab measurements.
- Spotting outliers with the IQR fence (1.5 × IQR beyond the quartiles).
- Averaging growth rates or ratios with the geometric mean.
Frequently asked questions
Which quartile method does this use?
The median-of-halves (Tukey-style, exclusive) method taught in most statistics courses: split the sorted data at the median, then take the median of each half, excluding the overall median itself when n is odd. Spreadsheet functions that interpolate can give slightly different values.
What if there is no repeated value?
Then the data has no mode and the calculator says so. If several values tie for the highest count, all of them are listed — data can be bimodal or multimodal.
Why is the geometric mean blank?
It is only defined when every value is greater than zero, because it multiplies the values together and takes the nth root. One zero or negative entry makes it undefined.
Sample or population SD — which row should I read?
Read sample if your list is a subset of a larger group you want to describe; read population if the list is the whole group. The sample version divides by n − 1 and is slightly larger.
How is the IQR used to find outliers?
A common fence marks values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as potential outliers. For the example (Q1 = 4, Q3 = 6, IQR = 2), the fences are 1 and 9, so nothing is flagged.