Mean Calculator (Average, Median, Mode, Range)

Find the arithmetic **mean (average)**, median, mode, range, and standard deviation of any set of numbers. Enter your data below and click 'Calculate' to see the full statistical breakdown.

How to Calculate the Mean (Average)

The **Mean**, also known as the arithmetic average, is the most common measure of central tendency. It is calculated using a simple formula:

Where $\sum x$ is the sum of all values in the data set, and $n$ is the count of values.

Media vs. Mediana: Quando Usare Quale?

• **Mean (Media):** Use when your data is symmetrically distributed and does not contain major outliers. It uses every value in the set.
• **Median (Mediana):** Use when your data is highly skewed by extreme outliers (e.g., in income or housing prices). The median is less affected by these extreme values, providing a better measure of the "typical" center.

What is Standard Deviation?

The **Standard Deviation** ($\sigma$) is the most widely used measure of data dispersion, or how "spread out" the numbers are from the mean. A low standard deviation means the numbers are tightly clustered around the mean; a high standard deviation means they are widely spread.

The **Variance** ($\sigma^2$) is the standard deviation squared.

Frequently Asked Questions (FAQ)

What is the formula for the Mean (Average)?

The formula is: **Mean = Sum of all values ($\sum x$) / Count of values ($n$)**.

How do you find the Mode if the list is multimodal?

If two or more numbers share the highest frequency, the data set is **multimodal**. For example, in the set $\{1, 1, 2, 3, 3, 4\}$, both 1 and 3 are the modes. Our calculator correctly handles and displays all modes.

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\text{Mean} (\bar{x}) = \frac{\sum x}{n}

$ \text{Mean} (\bar{x}) = \frac{\sum x}{n} $