# Standard Deviation and Standard Error

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Standard Deviation is defined as an absolute measure of dispersion of a series. It clarifies the standard amount of variation on either side of the mean. It is often misconstrued with the standard error, as it is based on standard deviation and sample size.

Standard Deviation is the square root of the average of squares of deviations from their mean. In other words for a given dataset, the standard deviation is the root-mean-square-deviation from arithmetic mean. Standard Deviation is a measure that quantifies the degree of dispersion of the set of observations. The farther the data points from the mean value, the greater is the deviation within the data set, representing that data points are scattered over a wider range of values and vice versa.

We might have observed that different samples with identical size, drawn from the same population, will give different values of statistic under consideration, i.e. sample mean. The Standard Error (SE) provides the standard deviation of the distribution of sample means for all the samples drawn from the population. It is used to make a comparison between sample means across the populations. In short, standard error of a statistic is nothing but the standard deviation of its sampling distribution. It has a great role to play the testing of statistical hypothesis and interval estimation. It gives an idea of the exactness and reliability of the estimate. The smaller the standard error, the greater is the uniformity of the theoretical distribution and vice versa.

The standard error is calculated by dividing standard deviation with square root of population size.

Standard Error for sample mean = σ/√n

Key Differences between Standard Deviation and Standard Error:

1. Standard Deviation is the measure which assesses the amount of variation in the set of observations. Standard Error gauges the accuracy of an estimate, i.e. it is the measure of variability of the theoretical distribution of a statistic.
2. Standard Deviation is a descriptive statistic, whereas the standard error is an inferential statistic.
3. Standard Deviation measures how far the individual values are from the mean value. On the contrary, how close the sample mean is to the population mean.
4. Standard Deviation is the distribution of observations with reference to the normal curve. As against this, the standard error is the distribution of an estimate with reference to the normal curve.
5. Standard Deviation is defined as the square root of the variance. Conversely, the standard error is described as the standard deviation divided by square root of sample size.
6. When the sample size is raised, it provides a more particular measure of standard deviation. Unlike, standard error when the sample size is increased, the standard error tends to decrease.