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Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, range and more from any data set. Free, browser-based, no signup.

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Descriptive Statistics Reference

Measure	Description
Mean	Sum of all values ÷ count (arithmetic average)
Median	Middle value when sorted; average of two middles for even n
Mode	Most frequently occurring value(s)
Range	Max − Min
Variance (pop.)	Average squared deviation from the mean
Std Dev (pop.)	Square root of variance — spread around the mean
Std Dev (sample)	Uses n−1 denominator (Bessel's correction)
IQR	Q3 − Q1 (interquartile range — middle 50% spread)

Population vs Sample Standard Deviation

Use population SD (σ) when your data is the entire group. Use sample SD (s) when your data is a sample drawn from a larger population — it corrects for the tendency to underestimate variability. Most real-world analysis uses sample SD.

'What does standard deviation tell me?', 'a' => 'Standard deviation measures the spread of data around the mean. A small SD means data points cluster tightly around the mean; a large SD means they are spread out. In a normal distribution, ~68% of data falls within ±1 SD of the mean.'], ['q' => 'What is IQR and why is it useful?', 'a' => 'The Interquartile Range (Q3 − Q1) covers the middle 50% of your data. It is resistant to outliers, unlike the range. IQR is used in box plots and to detect outliers: values beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR are considered outliers.'], ]" />