A sample of n = 25 scores has a mean of M = 40 and a variance of s2 = 100. What is the estimated standard error for the sample mean?

Question

What is the estimated standard error for the sample mean?

Answer 1

You probably have the formula for the standard error of the mean in your notes, right? It's just s/√n, where s is the sample standard deviation and n is the sample size. And you probably already know that the standard deviation s is (√variance), since the symbol for variance is s².

 

What does this mean in terms of basic concepts? 

• The standard deviation is the "spread-out-ness" or dispersion of the individual values or scores. When there is a lot of variation in the population, the variance is high and the average deviation from from the mean is high. 
• The standard error of the mean (aka standard error) is the "spread-out-ness" not of individuals but of sample means (averages). The larger your sample, the more accurate your average will be, right? It you take the average age of two people at random, you could easily get 50, 70, 30, or 10. However, if you take the average age of 100 people, you will almost always get something close to the true average in the population. The average error of the sample mean (i.e. standard error) is inversely proportional to the square root of the sample size, so quadrupling the size of the sample halves the standard error and makes the estimate twice as accurate.