Standard Error

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What is a 'Standard Error'

A standard error is the standard deviation of the sampling distribution of a statistic. Standard error is a statistical term that measures the accuracy with which a sample represents a population. In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error.

BREAKING DOWN 'Standard Error'

The term "standard error" is used to refer to the standard deviation of various sample statistics such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.

The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

The standard error is considered part of descriptive statistics. It represents the standard deviation of the mean within a dataset. This serves as a measure of variation for random variables, providing a measurement for the spread. The smaller the spread, the more accurate the dataset is said to be.

Standard Error and Population Sampling

When a population is sampled, the mean, or average, is generally calculated. The standard error can include the variation between the calculated mean of the population and once which is considered known, or accepted as accurate. This helps compensate for any incidental inaccuracies related the gathering of the sample.

In cases where multiple samples are collected, the mean of each sample may vary slightly from the others, creating a spread among the variables. This spread is most often measured as the standard error, accounting for the differences between the means across the datasets.

The more data points involved in the calculations of the mean, the smaller the standard error tends to be. When the standard error is small, the data is said to be more representative of the true mean. In cases where the standard error is large, the data may have some notable irregularities.

Standard Deviation and Standard Error

The standard deviation is a representation of the spread of each of the data points. The standard deviation is used to help determine validity of the data based the number of data points displayed within each level of standard deviation. Standard error functions more as a way to determine the accuracy of the sample or the accuracy of multiple samples by analyzing deviation within the means.