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Average Calculator

Calculate mean, median, mode, range, and standard deviation. Enter any set of numbers for complete statistical analysis.

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How to Calculate Average (Mean)

Add all values together and divide by the count: Mean = Sum ÷ Count. Enter numbers separated by commas, spaces, or new lines for complete statistical analysis.

Example

Dataset: 4, 7, 2, 9, 3

  • Mean: (4 + 7 + 2 + 9 + 3) ÷ 5 = 5.0
  • Median: Sorted: 2, 3, 4, 7, 9 → middle value = 4
  • Mode: No repeated values → no mode
  • Range: 9 − 2 = 7

Mean vs Median vs Mode

  • Mean (arithmetic average): Sum ÷ count. Sensitive to outliers — one extreme value shifts it significantly
  • Median (middle value): The value that splits the dataset in half when sorted. Resistant to outliers. For even-sized datasets, average the two middle values
  • Mode (most frequent): The value that appears most often. A dataset can have multiple modes (bimodal, multimodal) or no mode at all

When to Use Each

  • Mean: Symmetric data without outliers — test scores, heights, daily temperatures
  • Median: Skewed data with outliers — household income, home prices, response times. Median US household income (~$80,000) is far more representative than the mean (~$115,000) because extreme earners skew the average
  • Mode: Categorical or discrete data — most popular shoe size, most common survey response, most frequent error code

Standard Deviation

Measures how spread out values are from the mean. A low standard deviation means data is tightly clustered; a high one means data is spread wide.

  • 68% of data falls within 1 SD of the mean
  • 95% of data falls within 2 SDs of the mean
  • 99.7% of data falls within 3 SDs of the mean

This "68-95-99.7 rule" applies to normally distributed data and is used in quality control, grading curves, and scientific research.

Other Types of Averages

  • Weighted average: Values are multiplied by weights before summing. Used in GPA calculation (credits × grade points), portfolio returns, and overall course grades
  • Geometric mean: The nth root of the product of n values. Used for average growth rates, investment returns, and ratios
  • Harmonic mean: Reciprocal of the mean of reciprocals. Used for average speeds and rates

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Frequently Asked Questions

What is the difference between mean and median?

Mean is the sum divided by count (average). Median is the middle value when sorted. Median is less affected by extreme values.

When should I use median instead of mean?

Use median when data has outliers or is skewed. For example, median income is more representative than mean income.

What is mode?

Mode is the most frequently occurring value in a dataset. A dataset can have multiple modes or no mode.

What does standard deviation tell me?

Standard deviation measures how spread out the data is from the mean. Low SD means data is clustered near the mean.