## Sample Statistics Calculator

Calculates Sample Mean, Standard Deviation, Variance, and Standard Error.
Enter observations in box, use a separate line or comma between each measurement.

#### Sample Statistics (base n)

Sample has 2 observations.
Sample Mean: 39.5
Variance: 12.5
Standard Deviation: 3.5355339059327
Standard Error: 2.5

#### Population Statistics (base n-1)

Standard Deviation: 2.5
Variance: 6.25

### Tool Overview (Sample Mean Calculator, Sample Variance Calculator, Standard Error Calculator)

This sample statistics calculator look at a set of observations (the sample) and calculates the sample mean. We've added several other useful descriptive statistics (sample variance, standard deviation) to provide you with a simple statistics tool that you can use from your mobile phone. It is intended to replace several separate calculators: the sample mean calculator, a sample variance calculator, a standard error calculator, and a sample standard deviation calculator.

Enter your observations as a string of numbers - separated by commas or with a new line for each measurement. The sample mean calculator will calculate the mean - or average - value of the data you provide.

For the variance and standard deviation statistics, it is important to know if you are looking at a sample or the entire population of possible items. If we're looking at 10 items randomly pulled off an assembly line and measured, that would be a sample. If we take every child in the class and measure them, that would be the entire population. This is important because it affects which statistical formula we use to calculate variance and standard deviation.

For a sample, we calculate variance and standard deviation by using the number of items in the sample. If we're looking at the entire population, we reduce this by one (using n-1).

We also calculate a statistic known as the standard error, which depicts the expected difference between the sample mean and the real mean value of the underlying population. This differs from the standard deviation. The standard deviation captures the degree of scatter of the individual observations around the population mean. But the effects of this scatter are reduced as we take more samples. The standard error captures how far the sample means scatter around the true mean of that population. Different samples drawn from that same population would usually have different sample means, which effectively form a distribution of their own. This distribution can be associated with the standard deviation in the following manner: for a given sample size, the standard error is the standard deviation divided by the square root of the sample size. As sample size grows, the sample means will group more closely around the population mean and standard error decreases.

#### Sharing Results of The Sample Calculator

Need to pass an answer to a friend? It's easy to link and share the results of this calculator. Simply use the following format: