Our online standard deviation calculator determines the standard deviation, mean, variance, sum, coefficient of variance, statistical population, and error margin of the given set of data. Our sd calculator makes your calculations fast and gives accurate results.
“Standard deviation is the measurement of the variation between the given group or set of values.”
Our mean and standard deviation calculator online makes standard deviation calculations fast and accurate by using teh following equation:
$$ s = \sqrt{\dfrac{1}{N – 1} \sum_{i=1}^N\left(x_{i} – \bar{x}\right)^2} $$
Population standard deviation formula is:
$$ σ = \sqrt{\dfrac{1}{N} \sum_{i=1}^N\left(x_{i} – μ\right)^2} $$
Where
In order to understand how to find standard deviation of the mean, take a look at the example below.
The math test scores of different students are 51, 49, 45, 91, and 97. How to calculate standard deviation?
To find the standard deviation of the given class, we will find this with the help of the Sample standard deviation calculator formula:
$$ SD = σ = \sqrt\frac{\sum(x-µ)^2}{N} $$
µ = 51+49+45+91+94/5
µ = 330/5
µ = 66
| xi | xi-µ | (xi-µ)^2 |
|---|---|---|
| 51 | 51-66 = -16 | (-16)^2 = 256 |
| 49 | 49-66 = -17 | (-17)^2 = 289 |
| 45 | 45-66 = -21 | (-21)^2 = 441 |
| 91 | 91-66 = 25 | (25)^2 = 625 |
| 94 | 94-66 = 28 | (28)^2 = 784 |
| 2395 |
Finding standard deviation from mean:
SD = σ = 2395/5
SD = σ = 48.94
This standard deviation solver provides complete work with incredible speed. To use it, follow the steps below!
Input:
Output:
Our variance and standard deviation calculator online will give you the following results:
The standard deviation of the data is independent of any change in origin, but it depends on the change in the scale.
The standard deviation is inversely proportional to the mean of the sampling distribution. The standard deviation decreases as the sample size used to calculate the mean for sampling distribution increases.
From the source Wikipedia: Standard deviation, Basic examples, Definition of population values, Estimation, Identities, and mathematical properties.
From the source Khan Academy: sample standard deviation, Population, calculate sample standard deviation, sample variance.
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