What is the difference between population and sample standard deviation?

Population std dev (σ) divides by N; sample std dev (s) divides by N-1. Use sample std dev when your data is a sample from a larger population — which is almost always the case in practice.

What is the interquartile range (IQR)?

IQR = Q3 - Q1, where Q1 is the 25th percentile and Q3 is the 75th percentile. IQR is a robust measure of spread that is resistant to outliers, unlike standard deviation.

How is the median calculated with an even number of values?

With an even count, the median is the average of the two middle values. For [1, 3, 5, 7], the median is (3+5)/2 = 4.

The value that appears most frequently. A dataset can have no mode (all values unique), one mode (unimodal), or multiple modes (bimodal, multimodal).

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Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, and more from any dataset.

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About this tool

Enter a list of numbers to compute descriptive statistics: count, sum, mean, median, mode, range, variance, standard deviation, quartiles, and interquartile range. Shows a sorted dataset and frequency table. Useful for data analysis, grades, and research.

How to use

1 Enter numbers separated by commas, spaces, or new lines.
2 Statistics update automatically as you type.
3 See quartiles, outliers, and the sorted dataset.
4 Switch between population and sample standard deviation.

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