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

Mean is the arithmetic average (sum / count). Median is the middle value when data is sorted. Mode is the most frequently occurring value. Mean is best for symmetric data, median for skewed data with outliers, and mode for categorical data.

When should I use mean vs median?

Use the mean for symmetric data without outliers. Use the median when data has outliers or is skewed, as it is more resistant to extreme values.

How do outliers affect the mean?

Outliers significantly affect the mean because every value contributes equally. A single extreme value can pull the mean far from the center of most data points.

What is weighted mean and when should I use it?

Weighted mean assigns different importance (weights) to different values. Formula: Weighted Mean = Sum(value x weight) / Sum(weights). Use it when some values should count more than others.

Can the mean be negative or a decimal?

Yes. The mean can be any real number including negative, decimal, or zero. It reflects the mathematical average regardless of whether it matches an actual data point.

How is mean used in statistics and data analysis?

The mean is used to calculate variance and standard deviation, perform hypothesis testing, create confidence intervals, and build regression models. It is the basis for z-scores and normal distributions.

Statistics

Mean Calculator

Calculate the arithmetic mean (average) of a set of numbers with step-by-step solutions and detailed explanations

100% FreeStep-by-Step SolutionsEducational Explanations

Mean Calculator

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Numbers

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Try These Examples

Common real-world scenarios for calculating the mean

Test Scores

Numbers: 85, 92, 78, 90, 88

numbers: 85, 92, 78, 90, 88

Daily Sales

Numbers: 120, 150, 135, 180, 160

numbers: 120, 150, 135, 180, 160

Temperature (°F)

Numbers: 72, 68, 75, 70, 73

numbers: 72, 68, 75, 70, 73

With Decimals

Numbers: 3.5, 4.2, 3.8, 4.0, 3.9

numbers: 3.5, 4.2, 3.8, 4.0, 3.9

Large Numbers

Numbers: 1000, 1500, 1200, 1800, 1400

numbers: 1000, 1500, 1200, 1800, 1400

Mean Formula

The arithmetic mean (average) of n numbers is calculated by summing all values and dividing by the count:

\text{Mean} = \frac{x_1 + x_2 + \cdots + x_n}{n} = \frac{\sum_{i=1}^{n} x_i}{n}

Where $x_1, x_2, \ldots, x_n$ are the numbers and $n$ is the count.

Example:

Mean of 10, 20, 30 = (10 + 20 + 30) / 3 = 60 / 3 = 20

About the Mean

• The mean is the most common measure of central tendency

• It represents the "average" or "typical" value in a dataset

• Every value contributes equally to the calculation

• The mean is sensitive to outliers (extreme values)

• Used extensively in statistics, finance, and data analysis

Real-World Applications

📊 Academic Performance

Calculate average test scores, GPA, or class performance metrics

💰 Financial Analysis

Track average daily sales, monthly expenses, or investment returns

⚕️ Health Metrics

Monitor average blood pressure, heart rate, or weight measurements

🌡️ Environmental Data

Analyze average temperature, rainfall, or pollution levels

Common Mistakes to Avoid

❌ Ignoring Outliers

One extreme value can significantly skew the mean. Consider using median for skewed data.

❌ Mixing Units

Ensure all numbers use the same units (e.g., don't mix feet and inches).

❌ Division by Zero

You need at least one number to calculate a mean.

✅ Best Practice

Check for outliers and consider whether mean or median is more appropriate for your data.

Mean vs. Median vs. Mode: Which Should You Use?

Measure	Definition	Best Used When	Example
Mean	Sum divided by count	Data is symmetric with no outliers	Test scores: 80, 85, 90 → Mean = 85
Median	Middle value when sorted	Data has outliers or is skewed	Salaries: 40K, 45K, 200K → Median = 45K
Mode	Most frequent value	Categorical or discrete data	Shoe sizes: 8, 8, 8, 9, 10 → Mode = 8

Learn More About Mean, Median, and Mode

Khan Academy - Statistics

Free lessons on mean, median, mode, and summarizing quantitative data.

OpenStax Statistics Textbook

Open-source college-level textbook covering measures of central tendency.

Math is Fun - Mean, Median, Mode

Simple explanations with interactive examples for understanding averages.

Frequently Asked Questions

The mean is the sum of all values divided by the number of values. It represents the central tendency of a dataset. Formula: Mean = (x₁ + x₂ + ... + xₙ) / n. It's the most commonly used measure of average and provides a single number that represents the typical value in your data.

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