Calculate different types of averages: arithmetic, geometric, harmonic, and weighted averages with step-by-step solutions and explanations.
Calculate different types of averages: arithmetic, geometric, harmonic, and weighted averages:
Enter numbers separated by commas (e.g., 10, 20, 30)
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An average is a measure of central tendency that represents the typical value in a set of numbers. There are several types of averages, each with specific applications and mathematical properties. Understanding different types of averages is crucial in statistics, mathematics, and data analysis.
The most common types of averages are:
Choose from four different types of averages: arithmetic mean, geometric mean, harmonic mean, or weighted average.
Input your numbers separated by commas. For weighted average, also enter the corresponding weights.
The calculator will provide the average, step-by-step calculation, and detailed explanation.
The most common type of average, calculated by summing all values and dividing by the count.
Formula: (x₁ + x₂ + ... + xₙ) / n
Use for: General data analysis, test scores, temperatures
The nth root of the product of n values, useful for growth rates and ratios.
Formula: ⁿ√(x₁ × x₂ × ... × xₙ)
Use for: Investment returns, growth rates, ratios
The reciprocal of the arithmetic mean of reciprocals, useful for rates and speeds.
Formula: n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
Use for: Average speeds, rates, ratios of rates
Each value is multiplied by its weight, then divided by the sum of weights.
Formula: (w₁x₁ + w₂x₂ + ... + wₙxₙ) / (w₁ + w₂ + ... + wₙ)
Use for: Grade point averages, portfolio returns, survey results
Find the average of 10, 20, 30, 40
Solution: (10 + 20 + 30 + 40) / 4 = 100 / 4 = 25
Find the geometric mean of 2, 8, 32
Solution: ³√(2 × 8 × 32) = ³√(512) = 8
Grades: 85, 90, 78 with weights: 2, 3, 1
Solution: (85×2 + 90×3 + 78×1) / (2+3+1) = (170 + 270 + 78) / 6 = 86.33
Arithmetic mean for simple returns, geometric mean for compound returns, weighted average for portfolio performance.
Weighted averages for GPA calculations, arithmetic mean for test scores, harmonic mean for average speeds in physics.
Geometric mean for growth rates, harmonic mean for average speeds, arithmetic mean for measurements.
Weighted averages for customer satisfaction, arithmetic mean for sales data, geometric mean for growth rates.
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