Mean, Median, Mode Calculator

About the Mean, Median, Mode Calculator

The mean, median, and mode calculator computes all major measures of central tendency in one place. Enter your data to get the arithmetic mean (average), median (middle value), and mode (most frequent), along with the geometric mean, harmonic mean, root-mean-square, trimmed mean, and weighted mean.

Central tendency tells you where the "center" of your data lies. Different measures are appropriate for different situations — the mean works best for symmetric data, the median is robust to outliers and skewed distributions, and the mode identifies the most common value. This calculator computes all of them simultaneously, with a visual comparison showing exactly how they relate.

You also get a frequency table, skewness metrics (Fisher and Pearson), and an optional weighted mean for situations where not all data points are equally important. The sample data makes it easy to see how repeated values drive the mode while skewness pulls the mean away from the median.

When This Page Helps

It gives a comprehensive view of central tendency that no single measure can offer alone. By computing arithmetic, geometric, harmonic, trimmed, and weighted means alongside the median and mode, it helps you choose the right measure for your specific data and application.

The visual comparison chart and skewness metrics reveal the shape of your distribution at a glance — essential for choosing the right statistical tests and reporting the most representative summary of your data.

How to Use the Inputs

1. Enter numeric data separated by commas or spaces.
2. Set the number of decimal places for output precision.
3. Adjust the trim percentage for the trimmed mean calculation.
4. Optionally enter weights (one per data point) for the weighted mean.
5. Compare mean, median, mode, and the optional weighted mean in the visual comparison chart.
6. Check the skewness table to understand your data's symmetry.
7. Review the frequency table to see value counts.

Example Calculation

Tips & Best Practices

• When mean ≈ median, your data is approximately symmetric. When they diverge, the data is skewed.
• Use the geometric mean for rates of change (investment returns, population growth rates).
• Use the harmonic mean for rates (speed, throughput, price-to-earnings ratios).
• The trimmed mean is a compromise between mean and median — it removes a percentage of extremes before averaging.
• If your data is multimodal (2+ modes), consider whether it comes from a mixture of different populations.
• Weighted means are used in GPA calculations, portfolio returns, and any situation where observations have unequal importance.

Choosing the Right Average

The "best" average depends on your data and context. For symmetric data without outliers, the arithmetic mean is generally preferred — it uses all data and has the smallest standard error. For skewed data (income, property values), the median is more representative. For growth rates, use the geometric mean. For rates (speed, fuel economy), use the harmonic mean.

Mean–Median–Mode Inequality

For unimodal, moderately skewed distributions, an approximate relationship holds: Mode ≈ 3 × Median − 2 × Mean. This is Pearson's empirical rule. It's useful for estimating the mode when you only know the mean and median, but it breaks down for multimodal or highly skewed distributions.

Weighted Averages in Practice

Weighted means appear everywhere: GPA weights credit hours, stock indices weight by market cap (S&P 500) or price (Dow Jones), and quality metrics weight by importance. When calculating weighted means, ensure weights are meaningful and sum to a positive value. Negative weights can cause paradoxical results.

Frequently Asked Questions

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

  The mean (average) sums all values and divides by count — it uses every data point but is sensitive to outliers. The median is the middle value when data is sorted — it's robust to extreme values. The mode is the most frequently occurring value — it's the only measure that works for categorical data and identifies peaks in distributions.

• When should I use the median instead of the mean?

  Use the median when data is skewed (income, home prices, wait times) or contains outliers. For example, a neighborhood with nine $300K homes and one $10M mansion has a mean of $1.27M but a median of $300K — the median better represents the typical home price.

• What does "no mode" mean?

  If every value in your data appears exactly once, there is no mode — the data is called "amodal." This is common in continuous data with many unique values. Mode is most meaningful for discrete data or data that has been grouped into categories.

• What is the geometric mean used for?

  The geometric mean is used for multiplicative processes — compound interest rates, population growth rates, and any situation where you multiply rather than add. If an investment returns +10%, −5%, +20% over three years, the geometric mean gives the true average annual return, while the arithmetic mean overestimates it.

• What is a trimmed mean?

  A trimmed mean removes a percentage of the highest and lowest values before computing the average. A 10% trimmed mean drops the top 10% and bottom 10%. This makes the mean more resistant to outliers while still using most of the data, unlike the median which uses only the center value.

• How does skewness relate to mean and median?

  In positively (right) skewed data, the mean is pulled higher than the median by large outliers. In negatively (left) skewed data, the mean is pulled lower. The relationship mean > median suggests right skew, mean < median suggests left skew. Pearson's skewness coefficient formalizes this as 3(mean − median)/SD.