Sample Standard Deviation Calculator
Sample standard deviation calculator helps measure data spread from a sample. It quantifies variation in datasets, useful in statistics, research, and quality control. Investors use it for risk analysis, researchers for data reliability, and students for academic projects.
Formula
s = √[Σ(xᵢ - x̄)²/(n-1)]
Where:
s = sample standard deviation
x̄ = sample mean
n = number of data points
How to Use
1. Enter numbers separated by commas
2. Click Calculate
3. Get instant SD value
4. Review FAQs below results
5. Use Clear to reset
Derivation Process
1. Calculate mean (average)
2. Find squared differences from mean
3. Sum squared differences
4. Divide by (n-1) for sample variance
5. Take square root for SD
FAQs
Q1: Difference between sample and population SD?
Sample SD uses (n-1) denominator for unbiased estimate, while population SD uses N. This corrects bias in smaller samples (Bessel's correction).
Q2: Can I use spaces instead of commas?
No, only commas separate values. Invalid entries trigger alerts. Ensure format like "5,7,8.2,9".
Q3: Why is standard deviation important?
It measures data dispersion. Low SD means clustered data, high SD indicates spread. Crucial for statistical significance testing.
Q4: When to use sample SD?
When analyzing subset of population. Use population SD only if you have all data points.
Q5: How interpret SD value?
Compare with mean. SD=2 with mean=10 means most data between 8-12 (68% in normal distribution).
Q6: Can I calculate SD for non-numeric data?
No, requires numerical data. Text or categorical data will show error.
Q7: Alternatives to SD?
Range, variance, or IQR. But SD is most common for normal distributions.
Q8: Why decimal precision matters?
Precision depends on data context. Default is 4 decimals. Adjust using rounding as needed.
Q9: What if SD=0?
All values are identical. No variation in dataset.
Q10: Sample size impact?
Larger samples give more accurate SD. Small samples may underestimate population SD.