Statistics Calculator
Calculate mean, median, mode, quartiles, IQR, and skewness for any dataset in one all-in-one descriptive statistics summary.
How It's Calculated
Formula
\bar{x} = \frac{\sum x_i}{n} \qquad \text{IQR} = Q_3 - Q_1 \qquad g_1 = \frac{\frac{1}{n}\sum (x_i - \bar{x})^3}{\sigma^3}This calculator produces a complete descriptive-statistics summary for any dataset in one pass: count, mean, median, mode, minimum, maximum, range, the first and third quartiles (Q1 and Q3), the interquartile range (IQR), and skewness. Quartiles are computed using the exclusive method taught in most introductory statistics courses: sort the data, find the median (Q2), then take the median of the values strictly below it as Q1 and the median of the values strictly above it as Q3 — excluding the middle value itself when the count is odd. The IQR (Q3 − Q1) measures the spread of the middle 50% of the data and is far less sensitive to outliers than the full range. Skewness measures the asymmetry of a distribution: a value near 0 indicates a roughly symmetric dataset, a positive value indicates a longer tail on the right (a few unusually large values pulling the mean above the median), and a negative value indicates a longer tail on the left. This calculator reports the population moment coefficient of skewness (g1) — a specific, standard textbook definition — which can differ slightly from the sample-adjusted skewness formula (G1) used by some spreadsheet tools.
Worked Examples
Full summary for an odd-count dataset
- Dataset: 1, 2, 3, 4, 5, 6, 7, 8, 9 (n = 9)
- Mean = 45 / 9 = 5; Median (Q2) = 5 (the middle value)
- Lower half (excluding the median): 1, 2, 3, 4 → Q1 = (2+3)/2 = 2.5
- Upper half (excluding the median): 6, 7, 8, 9 → Q3 = (7+8)/2 = 7.5
- IQR = Q3 − Q1 = 7.5 − 2.5 = 5
- Range = max − min = 9 − 1 = 8
- This dataset is perfectly symmetric, so skewness = 0
Right-skewed dataset with an outlier
- Dataset: 1, 2, 2, 3, 3, 3, 4, 50 (n = 8)
- The single large outlier (50) pulls the mean well above the median
- Mean ≈ 8.5, Median = 3 — mean is noticeably larger than median
- Because the mean sits above the median with a long right tail, skewness is positive
Frequently Asked Questions
Why might my Q1/Q3 differ from another calculator's result?
Quartiles have several published, equally valid conventions (exclusive, inclusive, and interpolation-based methods) that can produce slightly different values for the same dataset. This calculator uses the exclusive method — the median of the lower half and the median of the upper half, excluding the overall median itself when the count is odd — which is the method most commonly taught in introductory statistics courses and used by TI-83/84 calculators.
What does a skewness value actually mean?
Skewness near 0 means the dataset is roughly symmetric around its mean. A positive skewness means the distribution has a longer tail stretching to the right — typically caused by a few unusually large values — which pulls the mean above the median. A negative skewness means the opposite: a longer left tail, with the mean pulled below the median.
Why is skewness reported as 0 when all my values are identical?
Skewness is mathematically undefined (0 divided by 0) when a dataset has zero spread, since the formula divides by the standard deviation cubed. This calculator reports 0 in that case by convention, since a dataset with no variation has no directional asymmetry to describe.
Why do I need at least 3 values?
Quartiles require a meaningful lower and upper half to split the data into, and skewness describes the shape of a distribution — neither concept is meaningful with only 1 or 2 points. This calculator requires at least 3 values so every reported statistic is meaningful.
How is this different from the Mean, Median, Mode calculator or the Standard Deviation calculator?
Those calculators each focus on one family of measures. This calculator combines mean, median, mode, quartiles, IQR, and skewness into a single all-in-one descriptive-statistics summary, so you don't need to run your dataset through multiple tools to see the full picture.
What happens if I enter a non-numeric or blank value?
The calculation is not performed and a clear message identifies which row is the problem, rather than silently dropping the row and quietly changing your dataset.