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Mean, Median & Mode Calculator β€” Full Descriptive Statistics

What is the average, middle, and most common value?

What This Does

Enter any list of numbers to instantly compute mean, median, mode, standard deviation, variance, range, skewness, and a frequency distribution table β€” the complete descriptive statistics toolkit for a dataset. Most calculators only give you mean and maybe median. This one computes all core measures of central tendency, dispersion, and distribution shape, plus a frequency table that shows how often each value appears and what percentage of the dataset it represents. The distribution shape analysis tells you whether your data is symmetric, right-skewed (long tail toward high values), left-skewed (long tail toward low values), or bimodal (two peaks) β€” context that affects which measure of center is most meaningful for your situation. When data is skewed, the median is a more robust measure of center than the mean because it is not pulled by extreme values. Understanding skewness matters for grading on a curve, analyzing salary data, or evaluating any dataset where outliers are common.

When Should You Use This?
  • β†’Analyzing a set of test scores, survey responses, or experimental measurements
  • β†’Checking whether a dataset is symmetric or skewed before choosing mean vs median for summaries
  • β†’Finding outliers β€” values far from the mean in a low-standard-deviation dataset
  • β†’Homework or exam prep for statistics, probability, or data analysis courses
  • β†’Quick descriptive analysis of small datasets without opening spreadsheet software
Example Scenario

You have 12 test scores: 45, 72, 78, 81, 83, 84, 85, 87, 88, 90, 92, 98. The mean is 81.9, median is 84.5, no mode (all unique). Standard deviation is 13.5. The distribution is slightly left-skewed (skewness = -0.62) due to the outlier at 45 pulling the mean below the median. Reporting the median (84.5) gives a better picture of typical performance than the mean (81.9) for this dataset.

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