Matemáticas

Average Calculator

Calculate mean, median, mode, standard deviation, variance, IQR, quartiles, and geometric mean. Paste any list of numbers — comma, space, or newline separated.

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9 statistical measuresNIST-verified formulasHistogram distributionUpdated July 2026

Enter numbers (comma, space, or newline separated)

Enter at least 2 numbers to see statistics.

Ejemplos prácticos

Student grade analysis: find the class average and spread

Paste 30 student scores separated by commas. The calculator instantly shows the mean (class average), median (middle score), standard deviation (spread), and a histogram showing score distribution — helping identify whether grades are clustered or spread across the range.

Property prices: mean vs median in a Dubai neighbourhood

In a neighbourhood with 9 apartments priced at AED 800k-900k and 1 penthouse at AED 8M, the mean price is AED 1.5M but the median is AED 850k. The median better represents what most buyers pay — the mean is distorted by the outlier.

Quality control: coefficient of variation for batch consistency

A manufacturing batch produces items with weights: 98.2, 99.1, 97.8, 100.4, 98.9, 99.7 grams. Mean = 99.02g, Std Dev = 0.84g, CV = 0.85% — well within the 2% tolerance threshold for this process.

Preguntas frecuentes

~5 min read

What is the arithmetic mean and how is it calculated?▾

The arithmetic mean is the sum of all values divided by the count of values. For example, the mean of 4, 7, 13, 2 is (4+7+13+2)/4 = 26/4 = 6.5. It is the most common type of average and what most people mean when they say 'average'.

When should I use median instead of mean?▾

Use the median when your data has outliers or is skewed. Property prices, salaries, and income data are classic examples — a small number of very high values pull the mean far above what most people experience. The median splits the dataset exactly in half and is not affected by extreme values.

What does standard deviation tell me?▾

Standard deviation (σ) measures how spread out the values are around the mean. A small standard deviation means values cluster tightly around the mean; a large one means they are spread wide. In a normal distribution, roughly 68% of values fall within 1 standard deviation of the mean, and 95% within 2.

What is the difference between population and sample standard deviation?▾

Population standard deviation (σ) divides by n (the total count) and is used when you have all the data. Sample standard deviation (s) divides by n-1 (Bessel's correction) and is used when your data is a sample from a larger population. This calculator uses the population formula (divides by n).

What is the geometric mean and when is it used?▾

The geometric mean is the nth root of the product of n values: GM = (x₁ × x₂ × … × xn)^(1/n). It is most useful for averaging rates of change, percentage growth, or ratios — such as compound annual growth rates (CAGR) or investment returns over multiple years. It can only be calculated for positive numbers.

What is the interquartile range (IQR)?▾

The IQR is the range of the middle 50% of your data: IQR = Q3 - Q1, where Q1 is the 25th percentile and Q3 is the 75th percentile. It is a robust measure of spread that ignores outliers. In box plots, values more than 1.5 × IQR beyond Q1 or Q3 are flagged as potential outliers.

What is the coefficient of variation (CV)?▾

CV = (Standard Deviation / Mean) × 100, expressed as a percentage. It shows the relative spread of data regardless of the unit or scale. A CV below 15% is generally considered low variability; above 30% is high. It is useful for comparing variability between datasets with different units or magnitudes.

What input formats does the calculator accept?▾

You can enter numbers separated by commas, spaces, semicolons, or new lines — or any mix of these. For example: '1,2,3' and '1 2 3' and '1\n2\n3' all produce the same result. Copy-pasting a column of numbers from Excel or a spreadsheet works directly.

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This calculator uses population standard deviation (divides by n), not sample standard deviation (divides by n-1). For sample data representing a larger population, divide the displayed variance by n and multiply by n-1 to get the sample variance.