Greatest common divisor and least common multiple
Find the largest integer dividing both numbers and the smallest positive multiple shared by them. These answer different grouping and cycle questions.
MAKE THE FORMULA CLEAR
Standard deviation and variance
Describe how spread out a list of numbers is around its mean. Both sample and population statistics are shown.
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Sample standard deviation s
2.13809
Use sample results for a sample, population results for all subjects. A larger standard deviation means more spread in this data set.
Population standard deviation σ2
Mean5
Number of data points8 records
Sample variance s²4.571429
Population variance σ²4
Worked steps
- 8 data points; mean = 5
- Sum of squared deviations from the mean = 32
- Sample: square root of (sum of squares ÷ (n−1)) = 2.13809
- Population: square root of (sum of squares ÷ n) = 2
Enter 2–200 numbers in the same unit, each with absolute value up to 1 billion. Commas separate data, not thousands; enter 1000 directly. Sample variance uses n−1 and population variance n as denominator; choose according to whether your data include the whole population. Displayed decimals are approximate. Descriptive statistics only, not an investment or medical conclusion.
Method and scope
Sum squared differences from the mean, divide by n for population variance or n-1 for sample variance, then take the square root for standard deviation. Choose the interpretation based on whether your data covers the whole population.
A smaller standard deviation means values are more tightly grouped on the same scale. Variance has squared units while standard deviation has the original data unit.
Use 2-200 numbers of one unit, each with absolute value at most one billion. Commas separate observations, so enter 1000 rather than 1,000 for one thousand; results are decimal approximations and are not investment or medical conclusions.
References:RMIT: data spread and sample/population formulas、NIST: sample standard deviation formula
What this helps you do
Describe how spread out a list of numbers is around its mean. Both sample and population statistics are shown.
What to enter
Start with numbers separated by commas, spaces, semicolons or new lines, then fill the other relevant fields in the units shown. The field hints explain the required format and examples.
How the calculation works
Sum squared differences from the mean, divide by n for population variance or n-1 for sample variance, then take the square root for standard deviation. Choose the interpretation based on whether your data covers the whole population.
Worked example
For 2,4,4,4,5,5,7,9 the mean is 5 and population standard deviation is 2. Sample standard deviation is about 2.13809.
Understanding the answer
A smaller standard deviation means values are more tightly grouped on the same scale. Variance has squared units while standard deviation has the original data unit.
Scope and limitations
Use 2-200 numbers of one unit, each with absolute value at most one billion. Commas separate observations, so enter 1000 rather than 1,000 for one thousand; results are decimal approximations and are not investment or medical conclusions.