The formula for standard error of the mean is equal to the ratio of the standard deviation to the root of sample size. SEM = SD/√N Where ‘SD’ is the standard deviation and N is the number of observations.
Full Answer
The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error of the mean.
The mean of the sample mean ˉX that we have just computed is exactly the mean of the population. The standard deviation of the sample mean ˉX that we have just computed is the standard deviation of the population divided by the square root of the sample size: √10=√20/√2.Feb 24, 2021
In case of decrease in sample size from 600 to 40, the standard error of the mean will be declined. Standard error equals the standard deviation divided by the square root of the sample size, so increase or decrease in sample size leads to fall or rise in the standard error.Nov 11, 2021
In other words, the SE gives the precision of the sample mean. Hence, the SE is always smaller than the SD and gets smaller with increasing sample size. This makes sense as one can consider a greater specificity of the true population mean with increasing sample size.Jul 25, 2019