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Mean, Median, Mode & Statistics Calculator

Compute comprehensive statistical descriptive metrics including mean, median, and mode.

Quick Answer:Paste any list of numbers. The calculator immediately computes the mean (sum/n), middle median, most frequent mode, and standard deviation.

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How to Use the Mean Calculator: Average, Median, Mode & Std Dev

1Paste or type your numbers into the input box separated by commas or spaces.
2Review the count (n), total sum, arithmetic mean, and median.
3Inspect the dataset modes and sample standard deviation (s).
4Use the metrics for academic homework, data analytics, or quality control.

Formula & How It Works

Descriptive Statistics Equations

Mean = ∑x / n; Sample Variance = ∑(x - μ)² / (n - 1); StdDev = √Variance

Computes central tendency and Bessel-corrected sample dispersion.

Worked Examples

Dataset Analysis: 2, 4, 4, 4, 5, 5, 7, 9

Input: 2, 4, 4, 4, 5, 5, 7, 9 (Count: 8)

Explanation: Sum is 40; 40 / 8 = 5; middle elements (4+5)/2 = 4.5; 4 appears most frequently.

Result: Mean = 5.000, Median = 4.500, Mode = 4, StdDev = 2.070

Frequently Asked Questions

When should you use median instead of mean?▼

The median is preferred for skewed distributions with extreme outliers, such as household income or real estate prices.

What is Bessel's correction in standard deviation?▼

Dividing by n - 1 instead of n corrects for the negative bias introduced when estimating population variance from a small sample.

Can a dataset have more than one mode?▼

Yes, if two or more values tie for the highest frequency, the dataset is bimodal or multimodal.

How is range defined in statistics?▼

The range is simply the difference between the maximum and minimum values in the dataset.

Quick Reference & Conversion Table

Metric	Formula	Sensitivity to Outliers	Description
Mean	∑x / n	High (pulled by extreme values)	Center of gravity of dataset
Median	Middle sorted value	Robust (unaffected by extremes)	50th percentile midpoint
Mode	Most frequent number	Robust	Peak frequency cluster
Sample StdDev	√(∑(x-μ)² / (n-1))	High	Average dispersion from mean

⚠️ Common Pitfalls to Avoid

•Confusing sample standard deviation (n-1 denominator) with population standard deviation (n denominator).
•Assuming every dataset has a single mode (datasets can be bimodal, multimodal, or have no mode).