Standard Deviation Calculator
Solve complex statistical calculations instantly.
Get **Standard Deviation, Variance, Quartiles**, and **Histogram Visualization** for free.
Tip: Data copied directly from Excel or Google Sheets can be pasted here and will be automatically recognized.
Ready for Analysis
Enter your data in the input box on the left and click the [Calculate] button. Your results will appear here.
Sample Standard Deviation (s)
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Used for most statistical analysis (divides by $n-1$)
Mean (Average)
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The central tendency of the data set
Data Distribution (Histogram)
Detailed Statistical Metrics
Population SD ($\sigma$)
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Sample Variance ($s^2$)
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Standard Error of Mean (SEM)
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Coefficient of Variation (CV)
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First Quartile (Q1)
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Median (Q2)
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Third Quartile (Q3)
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Interquartile Range (IQR)
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Data Count (N)
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Sum
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Range (Min ~ Max)
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Mode
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🧮 Calculation Process (Step-by-Step)
| No. | Value ($x_i$) | Deviation ($x_i - \mu$) | Deviation Squared ($(x_i - \mu)^2$) |
|---|---|---|---|
| Total | - | - | - |
1. Calculate Mean ($\mu$): Sum of values divided by the count.
2. Calculate Sum of Squares ($SS$): Sum of all squared deviations. Result:
3. Calculate Variance ($s^2$): Sum of Squares divided by $n-1$ (Sample) or $n$ (Population).
4. Calculate Standard Deviation ($s$): The square root of the Variance ($\sqrt{Variance}$).
Standard Deviation and Statistical Analysis Guide
📌 What is Standard Deviation?
Standard Deviation (SD) is a crucial measure of data dispersion, indicating how spread out the numbers are from the Mean (average). A low SD means the data points are generally close to the mean, while a high SD means the data points are spread out over a wider range.
- Sample SD ($s$): Used when the data set is a sample from a larger population (divides by $N-1$). This is the most common use case.
- Population SD ($\sigma$): Used when the data set includes every member of the population (divides by $N$).
📊 Quartiles and IQR Explained
Quartiles divide the data into four equal parts after sorting.
- Q1 (First Quartile): The point below which 25% of the data lies.
- Q2 (Median): The middle value, where 50% of the data lies.
- Q3 (Third Quartile): The point below which 75% of the data lies.
- IQR (Interquartile Range): $Q3 - Q1$. It represents the range of the middle 50% of the data, providing a robust measure of spread and helping identify outliers.
Frequently Asked Questions (FAQ)
Q. Is this tool truly free and safe to use?
A. Yes, it is 100% free with no hidden costs or subscriptions. More importantly, all calculations are performed locally in your browser (client-side JavaScript). **Your data is never sent to our servers** for processing, ensuring maximum privacy and security.
Q. Can I calculate large datasets?
A. Yes, while performance depends on your browser and device, the tool is optimized to handle tens of thousands of data points within a few seconds.