Standard deviation measures how spread out numbers are from the average. Low SD = data close together. High SD = data spread out. Example: test scores 70, 75, 80, 85, 90. Mean = 80. SD = 7.07. This means most scores are within 7 points of the average. Formula: SD = square root of (sum of squared differences from mean / n).
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📊 Standard Deviation Calculator
Calculate mean, variance, standard deviation, and more for any dataset. Perfect for statistics students, researchers, teachers, and data analysts. Shows complete step-by-step working!
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💡 Use Population if you have complete data. Use Sample if your data is a subset of a larger group (most common in research).
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The 365tool.net Standard Deviation Calculator uses standard statistical formulas with Bessel's correction for sample data. Free for students, researchers, and data analysts worldwide. No sign-up needed.
🤔 How Does This Work?
The Standard Deviation Calculator computes full descriptive statistics:
Mean = sum / count
Variance = sum of (each value - mean)² / (n or n-1)
Standard Deviation = square root of variance
Median = middle value when sorted
Mode = most frequent value
Range = maximum - minimum
❓ Frequently Asked Questions
What does standard deviation tell you?▼
Standard deviation tells you how spread out values are from the mean (average). SD = 0 means all values are identical. Small SD = values cluster close to the mean. Large SD = values are spread far from the mean. In test scores: small SD means most students scored similarly; large SD means scores varied widely.
What is the difference between population and sample SD?▼
Population SD: use when you have ALL data from the entire group (divide by n). Sample SD: use when your data is a subset of a larger population (divide by n-1). Using n-1 for samples gives a better estimate of the true population SD (Bessel's correction). In most research, use sample SD.
What is the 68-95-99.7 rule?▼
For normally distributed data: 68% of values fall within 1 SD of the mean, 95% within 2 SD, 99.7% within 3 SD. Example: heights with mean 170cm and SD 10cm: 68% of people are 160-180cm, 95% are 150-190cm, 99.7% are 140-200cm.
What is variance?▼
Variance = Standard Deviation squared. If SD = 7.07, variance = 50. Variance is used in statistical calculations but is harder to interpret directly because it is in squared units. Standard deviation (in original units) is easier to understand.
How is standard deviation used in business?▼
Quality control: SD measures product consistency. Finance: SD measures investment volatility (risk). Human resources: SD of employee salaries shows pay equity. Marketing: SD of survey scores shows how consistent customer opinions are. Lower SD usually means more consistent/predictable outcomes.
Standard deviation tells you how spread out values are from the mean (average). SD = 0 means all values are identical. Small SD = values cluster close to the mean. Large SD = values are spread far from the mean. In test scores: small SD means most students scored similarly; large SD means scores varied widely.
What is the difference between population and sample SD?▼
Population SD: use when you have ALL data from the entire group (divide by n). Sample SD: use when your data is a subset of a larger population (divide by n-1). Using n-1 for samples gives a better estimate of the true population SD (Bessel's correction). In most research, use sample SD.
What is the 68-95-99.7 rule?▼
For normally distributed data: 68% of values fall within 1 SD of the mean, 95% within 2 SD, 99.7% within 3 SD. Example: heights with mean 170cm and SD 10cm: 68% of people are 160-180cm, 95% are 150-190cm, 99.7% are 140-200cm.
What is variance?▼
Variance = Standard Deviation squared. If SD = 7.07, variance = 50. Variance is used in statistical calculations but is harder to interpret directly because it is in squared units. Standard deviation (in original units) is easier to understand.
How is standard deviation used in business?▼
Quality control: SD measures product consistency. Finance: SD measures investment volatility (risk). Human resources: SD of employee salaries shows pay equity. Marketing: SD of survey scores shows how consistent customer opinions are. Lower SD usually means more consistent/predictable outcomes.