This is a simplified version of our descriptive statistics tool which calculates the sample mean and the associated standard error. It is designed for professionals who only need this statistic.

The standard error of a parameter is defined as the standard deviation of the sampling distribution. A sampling distribution is the expected distribution of that statistic if you took multiple samples from the underlying population. So the sampling distribution of the sample mean would be the distribution of the means of repeated samples from a population. The standard deviation of this sampling distribution is the standard error of the sample mean.

The standard error can be used to develop confidence intervals for the unknown population mean. It can be used to assess the degree of precision of your estimate or measurement process. The relative standard error of a survey can be computed as the ratio of its standard error to the sample mean. A lower relative standard error indicates higher precision in the findings between studies, regardless of any differences in the sample mean. This is commonly used to set standards of significant for scientific review and publication processes; supporting surveys must satisfy a certain level of precision and reliability in their findings to quality for publication.

This tool is developed so you can save your data and use it in our other calculators. Simply hit "save data" and enter a name for this data set. It will be added to the menu shown alongside (or below) the calculators. When you open another page on our site, you will see a list of saved datasets. Simply click on that item and it will pre-populate the calculator box.

A standard deviation calculator is a tool that calculates the measure of the amount of variation or dispersion in a set of data. It is a commonly used measure of the spread of a statistical distribution. The standard deviation is used to quantify the amount of variation or dispersion in a set of data.

To use a standard deviation calculator, you need to input the set of observations from your sample. The calculator will then calculate the standard deviation by taking the square root of the variance of the sample, which is the average of the squared differences from the mean.

For example, if you have a sample of 10 observations with values of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, the standard deviation calculator will calculate the standard deviation as follows:

Step 1: Calculate the mean

(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) / 10 = 10

Step 2: Calculate the variance

((2-10)^2 + (4-10)^2 + (6-10)^2 + (8-10)^2 + (10-10)^2 + (12-10)^2 + (14-10)^2 + (16-10)^2 + (18-10)^2 + (20-10)^2) / 10 = 33.2

Step 3: Calculate the standard deviation

Square root of 33.2 = 5.76

Therefore, the standard deviation for this sample is 5.76.

The standard deviation is a fundamental concept in statistics because it provides a measure of the amount of variation or dispersion in a set of data. It is useful in many statistical analyses, including hypothesis testing, confidence interval estimation, and regression analysis.

Additionally, the standard deviation is used to calculate other important statistics, such as the coefficient of variation and the standard error of the mean. The coefficient of variation is a measure of the relative variability of a set of data, while the standard error of the mean is a measure of the precision of the sample mean as an estimator of the population mean.

The standard deviation can also be used to identify outliers in a set of data. An outlier is an observation that is significantly different from the other observations in the sample. Outliers can greatly influence the mean and other statistics, so it is important to identify and investigate them when analyzing data.

The standard deviation of a sample is influenced by several factors, including the range of values in the sample, the presence of outliers, and the sample size. A larger range of values or the presence of outliers will result in a larger standard deviation, while a smaller range of values or the absence of outliers will result in a smaller standard deviation.

Additionally, as the sample size increases, the standard deviation becomes a more reliable estimator of the population standard deviation. This is because larger sample sizes provide more information about the underlying population distribution and reduce the effect of random variation in the sample.

It is important to note that the standard deviation is a measure of the spread of the data, not the shape of the distribution. Different distributions can have the same standard deviation, so it is important to consider other statistics, such as the skewness and kurtosis, to fully understand the shape of the distribution.

A standard deviation calculator is a useful tool for calculating the measure of the amount of variation or dispersion in a set of data. The standard deviation is a fundamental concept in statistics that provides a measure of the spread of a statistical distribution. It is used in many statistical analyses and can be influenced by several factors, including the range of values in the sample, the presence of outliers, and the sample size. By understanding how to use a standard deviation calculator and the significance of standard deviation in statistics, you can make more informed decisions based on your data.