When sample standard deviation (s) is used as an estimate of σ (when it is unknown), the estimated standard error of the mean is s/N 1/2. The standard error would drop as the sample size increased, which agrees with the information above. Note that if you took a sample size of 50, the standard error would then be: σ m = 10 / 50 1/2 = 1.4142. This means that if you took all possible samples of size 30 from the class, the mean of all those samples would be 62 and the standard error would be 1.8257. Since n = 30, the standard error of the sample mean is: σ m = 10/30 1/2 = 1.8257. Calculate the standard error of the sample mean and interpret your results. A sample of 30 students is taken from the class. Suppose that the mean grade of students in a class is 62%, with a standard deviation of 10%. More specifically, the size of the standard error of the mean is inversely proportional to the square root of the sample size. The formula shows that the larger the sample size, the smaller the standard error of the mean. However, many of the uses of the formula do assume a normal distribution. This formula does not assume a normal distribution. Where σ is the standard deviation of the original distribution and N is the sample size (the number of scores each mean is based upon). The formula for the standard error of the mean is: It is the standard deviation of the sampling distribution of the mean. The standard error of the mean is designated as: σ m. The standard error of a statistic is usually designated by the Greek letter sigma (σ) with a subscript indicating the statistic. In general, the larger the sample size, the smaller the standard error. The standard error of a statistic depends on the sample size. The inferential statistics involved in the construction of confidence intervals and significance testing are based on standard errors. Standard errors are important because they reflect how much sampling fluctuation a statistic will show.
The standard error of a statistic is the standard deviation of the sampling distribution of that statistic.
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