If the sample size increases while the variability remains the same, then the standard error decreases.
Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.
SE = SD / √n
where SE = standard error
SD = sample standard deviation
n = sample size
Variability refers to the statistical dispersion of data which is expressed through the range, variance, or standard deviation.
Increasing the sample size, n, while having the same variability, will result to a lower value for the standard error.
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