Average Calculator | Mean, Median, Mode & Range Calculator

📖 How to Use This Average Calculator

Enter your numbers - Type or paste a list of numbers in the text area.

Separate values - Use commas, spaces, or both (e.g., "10, 20, 30" or "10 20 30").

Click "Calculate Statistics" - Get instant results for mean, median, mode, range, sum, and count.

📊 Understanding Statistical Measures

Mean (Average) is the sum of all values divided by the number of values. It's the most common measure of central tendency, but can be skewed by outliers (extremely high or low values).

Median is the middle value when numbers are sorted in order. It's less affected by outliers and better represents typical values for skewed distributions (like income data).

Mode is the value that appears most frequently. Data sets can have one mode (unimodal), two modes (bimodal), or more (multimodal).

Range is the difference between the highest and lowest values, showing the spread of your data.

🧮 Formulas Used

Mean = (x₁ + x₂ + ... + xₙ) ÷ n
Median = Middle value of sorted data
Mode = Most frequent value(s)
Range = Max(x) - Min(x)

💡 When to Use Each Measure

Use Mean when: Data is normally distributed without extreme outliers
Use Median when: Data has outliers or is skewed (e.g., income, house prices)
Use Mode when: Analyzing categorical data or finding most common value
Use Range when: Understanding the spread or variability of your data

❓ Frequently Asked Questions (FAQ)

What is the difference between mean, median, and mode?

Mean is the arithmetic average (sum ÷ count). Median is the middle value when sorted. Mode is the most frequent value. For symmetric distributions, they are similar; for skewed data, median is often more representative.

Why is the median sometimes better than the mean?

The median is resistant to outliers. For example, in a neighborhood where most houses cost $300,000 but one costs $3,000,000, the mean would be skewed high ($570,000), while the median ($300,000) better represents typical home prices.

What does it mean if there are multiple modes?

Multiple modes indicate that several values occur with the same highest frequency. This is common in bimodal distributions (two peaks) or multimodal data.

Can I use decimal numbers?

Yes! The calculator supports decimals (e.g., 10.5, 20.75) and negative numbers as well.

What is the range telling me about my data?

Range shows how spread out your data is. A small range means values are clustered together; a large range indicates wide variability.

How many numbers can I input?

The calculator can handle thousands of numbers efficiently. There's no practical limit for typical use cases.