Standard deviation and standard error are two important concepts in statistics, and while they may sound similar, they serve different purposes.
Standard Deviation is a measure of the amount of variation or dispersion of a set of values. It indicates how spread out the numbers are in a data set. A low standard deviation means that the values tend to be close to the mean (average) of the set, whereas a high standard deviation means that the values are spread out over a wider range. Standard deviation provides insight into the variability of individual data points.
Standard Error, on the other hand, is a measure of how much the sample mean (average) of a data set is expected to vary from the true population mean. Essentially, it reflects the accuracy of the sample mean as an estimate of the population mean. The standard error is calculated by dividing the standard deviation by the square root of the sample size (n). As the sample size increases, the standard error decreases, indicating a more precise estimate of the population mean.
In summary, standard deviation pertains to the variability of individual data points within a sample, while standard error pertains to the variability of a sample mean as an estimate of the population mean.