Statistics Calculator
指导
Statistics Calculator
Calculate comprehensive descriptive statistics for any dataset. Paste or type a list of numbers and instantly get mean, median, mode, standard deviation, variance, quartiles, skewness, kurtosis, and more. Includes a histogram visualization, frequency distribution table, five-number summary, and the option to toggle between population and sample calculations. Export your results as CSV.
如何使用
Enter or paste your numbers into the text area. The calculator auto-detects delimiters including commas, spaces, newlines, semicolons, and tabs, so you can paste directly from spreadsheets or CSV files. Toggle between population and sample mode to adjust variance and standard deviation calculations. All statistics update in real time. Use the histogram to visualize the distribution and export everything as CSV for further analysis.
特征
- Full Descriptive Statistics – Count, sum, mean, median, mode(s), range, min, max, quartiles, IQR, variance, standard deviation, standard error, coefficient of variation
- Advanced Measures – Skewness and kurtosis for distribution shape analysis
- Population vs Sample Toggle – Switch between population (divide by n) and sample (divide by n-1) calculations for variance and standard deviation
- Histogram Visualization – Canvas-based bar chart with automatic bin calculation using Sturges’ rule
- Frequency Distribution – Table showing each unique value and its count
- Five-Number Summary – Min, Q1, median, Q3, max at a glance
- Auto-Detect Delimiters – Paste from spreadsheets, CSV files, or plain text lists
- CSV 导出 – Download all calculated statistics as a CSV file
常问问题
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What is the difference between population and sample standard deviation?
Population standard deviation divides the sum of squared deviations by n (the total count), while sample standard deviation divides by n-1. The n-1 correction, called Bessel's correction, accounts for the fact that a sample underestimates the true population variability. Use population when your data includes every member of the group you are analyzing. Use sample when your data is a subset drawn from a larger population. For most real-world datasets where you are working with a sample, n-1 is the correct choice.
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What do skewness and kurtosis tell you about data?
Skewness measures the asymmetry of a distribution. A skewness of 0 means the data is symmetric. Positive skewness means the right tail is longer (data skewed right), while negative skewness means the left tail is longer. Kurtosis measures how heavy the tails are compared to a normal distribution. A normal distribution has kurtosis of 3 (excess kurtosis of 0). Higher kurtosis means heavier tails and more outliers. These measures help you understand the shape of your data beyond what mean and standard deviation reveal.
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How are quartiles calculated?
Quartiles divide sorted data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 (50th percentile) is the overall median, and Q3 (75th percentile) is the median of the upper half. The interquartile range (IQR) is Q3 minus Q1 and represents the middle 50% of the data. IQR is useful for identifying outliers: values below Q1 minus 1.5 times IQR or above Q3 plus 1.5 times IQR are typically considered outliers. This calculator uses the inclusive method for quartile computation.
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What is the coefficient of variation and when should I use it?
The coefficient of variation (CV) is the standard deviation divided by the mean, expressed as a percentage. It measures relative variability, making it useful for comparing the spread of datasets with different units or vastly different means. For example, comparing the variability of heights (measured in centimeters) with weights (measured in kilograms) is meaningless using standard deviation alone, but CV allows a fair comparison. A CV below 15% generally indicates low variability, while above 30% suggests high variability.
