Compute mean, median, mode, range, variance and standard deviation.
Enter numbers separated by commas, spaces, or new lines.
Mean
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Median
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Mode
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Range
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Variance
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Std Dev
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Min
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Max
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Count
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The Statistics Calculator computes the most common descriptive statistics for any data set in a single operation. Paste your numbers separated by commas, spaces, or line breaks, and the calculator instantly returns the mean, median, mode, range, variance, standard deviation (sample), minimum, maximum, and count. This is the Swiss army knife of basic data analysis — useful for everything from analyzing test scores to summarizing scientific measurements.
Mean = Σx ÷ n
For odd n: middle value of sorted data. For even n: average of the two middle values.
The value(s) that appear most often. There may be one mode, multiple modes, or no mode (if all values are unique).
s² = Σ(x − mean)² ÷ (n − 1)
s = √variance = √( Σ(x − mean)² ÷ (n − 1) )
Consider the data set: 85, 92, 78, 90, 88, 95, 82.
Mean, median, and mode each tell you something different about your data. The mean is the most familiar but is sensitive to outliers — a single billionaire in a sample of teachers will pull the mean income far above what most people actually earn. The median is robust to outliers and is the preferred measure for skewed data like income, house prices, and reaction times. The mode is most useful for categorical data (e.g., the most common eye color in a class).
For symmetric distributions like height or IQ scores, mean and median are nearly equal and either works. For right-skewed data (long tail on the high end) like income, mean > median. For left-skewed data (long tail on the low end) like retirement age, mean < median. Always report both mean and median to give readers a complete picture of central tendency.
Two data sets can have the same mean but very different spread. The set {4, 5, 6, 5, 5} and the set {1, 9, 1, 9, 5} both have mean 5, but the second is far more variable. Standard deviation quantifies this spread: the first has SD ≈ 0.71, the second has SD ≈ 3.74. In academic contexts, SD helps you understand whether a test score of 85 is exceptional (high SD) or typical (low SD).
In a normal (bell-curve) distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three. This "empirical rule" is the foundation of grading curves, quality control, and statistical inference. A test score one SD above the mean is roughly the 84th percentile — a useful benchmark for interpreting your own performance relative to a group.
Mean is the arithmetic average (sum ÷ count). Median is the middle value when sorted. Mode is the most frequent value. For symmetric data they are equal; for skewed data they differ.
Standard deviation measures how spread out the data is from the mean. A low SD means data clusters near the mean; a high SD means data is widely spread. It is the square root of variance.
Population SD divides by N; sample SD divides by N−1. Use sample SD when your data is a sample from a larger population. The calculator supports both.
Quartiles divide sorted data into four equal parts. Q1 is the 25th percentile, Q2 is the median (50th), Q3 is the 75th. The interquartile range (IQR) = Q3 − Q1 measures the middle 50% spread.
Variance is the average squared deviation from the mean. A variance of 0 means all values are identical. Larger variance means more spread. Variance is in squared units, which is why we usually prefer standard deviation (same units as the data).
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