Editing Standard error (section)

===Standard error of mean versus standard deviation===
In scientific and technical literature, experimental data are often summarized either using the mean and standard deviation of the sample data or the mean with the standard error. This often leads to confusion about their interchangeability. However, the mean and standard deviation are [[descriptive statistics]], whereas the standard error of the mean is descriptive of the random sampling process. The standard deviation of the sample data is a description of the variation in measurements, while the standard error of the mean is a probabilistic statement about how the sample size will provide a better bound on estimates of the population mean, in light of the central limit theorem.<ref>{{cite journal | first = M. | last = Barde | year = 2012 | title = What to use to express the variability of data: Standard deviation or standard error of mean? | journal = [[Perspect. Clin. Res.]] | volume = 3 | issue = 3 | pages = 113–116 | doi = 10.4103/2229-3485.100662 | pmid = 23125963 | pmc = 3487226 | doi-access = free }}</ref>

Put simply, the '''standard error''' of the sample mean is an estimate of how far the sample mean is likely to be from the population mean, whereas the '''standard deviation''' of the sample is the degree to which individuals within the sample differ from the sample mean.<ref>{{cite book |first=Sylvia |last=Wassertheil-Smoller |author-link=Sylvia Wassertheil-Smoller |title=Biostatistics and Epidemiology : A Primer for Health Professionals |location=New York |publisher=Springer |edition=Second |year=1995 |isbn=0-387-94388-9 |pages=40–43 |url=https://books.google.com/books?id=-PHiBwAAQBAJ&pg=PA40 }}</ref> If the population standard deviation is finite, the standard error of the mean of the sample will tend to zero with increasing sample size, because the estimate of the population mean will improve, while the standard deviation of the sample will tend to approximate the population standard deviation as the sample size increases.