Comprehensive statistics calculator for any dataset. Calculates mean, median, mode, range, variance, standard deviation, quartiles (Q1/Q3), IQR, geometric mean, and more — with step-by-step working and a visual frequency histogram.
Type or paste numbers separated by commas, spaces, or new lines. Decimals and negative numbers are supported. The count and sorted list update in real time as you type.
All measures calculate simultaneously: count, sum, mean, median, mode(s), range, minimum, maximum, Q1, Q3, IQR, variance (population and sample), standard deviation, coefficient of variation, geometric mean, and harmonic mean.
Click any statistic to expand the step-by-step explanation for that measure. The frequency histogram visualises the data distribution with the mean, median, and mode marked as coloured lines. All results are copyable.
Mean is the arithmetic average — sum all values and divide by count. It is sensitive to outliers (a single extreme value heavily affects it). Median is the middle value when data is sorted — it is robust to outliers and better represents the "typical" value in skewed distributions. Mode is the most frequently occurring value — useful for categorical data and understanding the most common outcome. When a distribution is symmetric, all three are equal. In skewed distributions they differ significantly.
Quartiles divide a sorted dataset into four equal parts. Q1 (first quartile) is the median of the lower half — 25% of data falls below it. Q2 is the median — 50% of data falls below it. Q3 (third quartile) is the median of the upper half — 75% of data falls below it. The Interquartile Range (IQR = Q3 - Q1) measures the spread of the middle 50% of the data and is used to identify outliers: values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered outliers.
The geometric mean is the Nth root of the product of N values: ⁿ√(x₁ × x₂ × ... × xₙ). It is appropriate for data that represents rates of change, ratios, or percentages. For example, investment returns over multiple years should be averaged using geometric mean, not arithmetic mean. If an investment returns 50% in year 1 and -50% in year 2, the arithmetic mean is 0% (suggesting no change), but the geometric mean is -13.4%, correctly showing a loss.
A dataset has no mode when all values occur exactly once — no value repeats. A dataset has multiple modes when two or more values are tied for the highest frequency (a bimodal or multimodal distribution). Multimodal distributions often indicate the presence of distinct subgroups within the data (for example, a height dataset mixing men and women might show two modes near the typical male and female heights).
Range = maximum value - minimum value. It is the simplest measure of spread, indicating the total extent of the data. A large range suggests high variability; a small range suggests the data is tightly clustered. The weakness of range is that it is highly sensitive to outliers — a single extreme value can produce a large range even if most data points are closely clustered. The IQR is a more robust alternative because it ignores the most extreme values.
The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals: n ÷ Σ(1/xᵢ). It is appropriate for rates and speeds. For example, if you drive 60 km at 30 km/h and 60 km at 60 km/h, the average speed is the harmonic mean of 30 and 60: 2 ÷ (1/30 + 1/60) = 40 km/h, not the arithmetic mean of 45 km/h. The harmonic mean is always ≤ geometric mean ≤ arithmetic mean (AM–GM–HM inequality).
