how do you find the standard error of the sample mean
Standard error Therefore, the relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean.
Mean The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution. In this context, it is also known as the expected value. For a discrete probability distribution, the mean is given by   ∑ x P ( x )  {\displaystyle \textstyle \sum xP(x)} , where the sum is taken over all possible values of the random variable and   P ( x )  {\displaystyle P(x)}  is the probability mass function. For a continuous distribution,the mean is    ∫ − ∞  ∞  x f ( x ) d x  {\displaystyle \textstyle \int _{-\infty }^{\infty }xf(x)\,dx} , where   f ( x )  {\displaystyle f(x)}  is the probability density function. In all cases, including those in which the distribution is neither discrete nor continuous, the mean is the Lebesgue integral of the random variable with respect to its probability measure. The mean need not exist or be finite; for some probability distributions the mean is infinite (+∞ or −∞), while others have no mean.