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Enter a list of numbers to calculate mean, median, mode, range, sum, count, geometric mean, harmonic mean, and quartiles.
Central Tendency Formulas:
Arithmetic Mean: x̄ = (sum of all values) / n
Geometric Mean: G = (x₁ × x₂ × ... × xₙ)^(1/n)
Harmonic Mean: H = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
IQR = Q3 - Q1
Mean is the arithmetic average (sum divided by count). Median is the middle value when sorted. Mode is the most frequent value. For symmetric distributions they are equal; for skewed data they differ.
Use geometric mean when averaging growth rates, ratios, or percentages. If an investment grows by 10%, 20%, and 5% in three years, the geometric mean gives the equivalent annual rate. It requires all positive values.
The harmonic mean is useful for averaging rates such as speeds. If you travel equal distances at 60 mph and 40 mph, the average speed is the harmonic mean: 2 / (1/60 + 1/40) = 48 mph, not 50 mph.
The IQR is Q3 - Q1, the range covering the middle 50% of the data. It is resistant to outliers. Values more than 1.5 × IQR below Q1 or above Q3 are often considered outliers.
If every value in the dataset appears exactly once, there is no mode. Mode is only meaningful when at least one value repeats more than others. A dataset can also be bimodal (two modes) or multimodal (many modes).