Mean, Median & Mode Calculator — Full Descriptive Statistics
What is the average, middle, and most common value?
Mean, Median & Mode Calculator
Enter numbers separated by commas, spaces, or semicolons. Mean, median, mode, standard deviation, quartiles, skewness, CDF and charts all update live as you type.
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Enter any list of numbers to instantly compute mean, median, mode, standard deviation, variance, range, skewness, and a frequency distribution table — 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) — 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.
- →Analyzing a set of test scores, survey responses, or experimental measurements
- →Checking whether a dataset is symmetric or skewed before choosing mean vs median for summaries
- →Finding outliers — values far from the mean in a low-standard-deviation dataset
- →Homework or exam prep for statistics, probability, or data analysis courses
- →Quick descriptive analysis of small datasets without opening spreadsheet software
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.
What is the difference between mean, median, and mode?
The mean (arithmetic average) adds all values and divides by count — it's sensitive to outliers. The median is the middle value when data is sorted — it's robust to outliers. The mode is the most frequently occurring value — useful for categorical or discrete data. For symmetric distributions these three are roughly equal. For skewed distributions (like incomes), the median better represents the 'typical' value because the mean gets pulled toward extreme values.
What does standard deviation tell me?
Standard deviation measures how spread out values are around the mean. A small SD means values cluster tightly near the mean; a large SD means values are widely spread. For roughly bell-shaped distributions, about 68% of values fall within one SD of the mean, and about 95% fall within two SDs. This makes SD useful for identifying outliers: a value more than 2 SDs from the mean is unusual.
What is the difference between sample and population standard deviation?
Population SD divides by n (all members of the group). Sample SD divides by n-1 (Bessel's correction), which corrects for the fact that a sample tends to underestimate the true spread. Use sample SD (n-1) when your data is a sample drawn from a larger population. Use population SD (n) only when your dataset is the entire population — for example, all students in a class rather than a random selection.
What does it mean if data is skewed?
Right-skewed (positive skew) means a long tail extends toward high values, with most values clustered on the left — common in income data, house prices, and reaction times. Left-skewed (negative skew) means a long tail toward low values. When data is skewed, the mean is pulled toward the tail while the median stays near the center of the bulk of data. For reporting purposes, the median is usually more representative of skewed data.
What is a bimodal distribution?
A bimodal distribution has two peaks — two values (or ranges) that appear more frequently than those around them. This often indicates two distinct subgroups in the data. For example, test scores for a class might be bimodal if half the students studied and half didn't, producing two clusters. When data is bimodal, neither the mean nor median captures the distribution shape well — it's worth investigating what the two groups represent.