🧮 Math
Standard Deviation Calculator
Paste numbers and get mean, median, mode, variance, standard deviation, and more. Population or sample.
Count
12
Sum
87
Mean
7.25
Median
7
Mode
7
Min
1
Max
15
Range
14
Variance
18.75
Std Dev
4.330127
Coeff of Variation
59.72589%
[ Ad · 728×90 ]
Related Tools
Percentage Calculator
Calculate percentages, percentage change, and what percent o...
Random Number Generator
Generate random numbers in any range. Single number, list, o...
Correlation Calculator
Enter two sets of numbers and calculate Pearson correlation ...
Sample Size Calculator
Calculate the required sample size for any survey or experim...
Population vs sample standard deviation
Population (σ): Use when your data represents the entire population. Divides by N.
Sample (s): Use when your data is a sample from a larger population. Divides by N−1 (Bessel's correction). This is the most common choice in practice.
Formulas used
- Mean = Σx / N
- Variance (sample) = Σ(x − mean)² / (N−1)
- Std Dev (sample) = √Variance
- Median = middle value when sorted
- Mode = most frequently occurring value
What does standard deviation tell you?
A low SD means values are clustered close to the mean. A high SD means values are spread out. In a normal distribution, ~68% of values fall within 1 SD of the mean, and ~95% within 2 SDs.