Standard error of the mean: practice exercises
The standard error of the mean (SEM)
What is the standard error of the mean (SEM)?The standard error of the mean (SEM) is an estimate of the standard deviation of a curve that would be graphing means of samples repeatedly taken. It is used routinely on graphs and tables (e. g. Mean=23.5 $\pm{1.25}$) of means of actual experimental data. This is the most difficult concept in Statistics! A simple and clear explanation is given here.
The problem
A couch wants to know the mean (average) height of male freshmen. He also wants to know how much these heights vary, and how reliable the mean is, that is will he get approximately the same mean if he measures again? He took a sample and measured their heights in cm.$X$
!.88
1.86
2.00
11.9
1.78
1.85
1,87
198
1.82
1.90
1.76
The formula for SEM is simple: ....next
$$SEM={σ\over\sqrt{n}}$$
He will calculate the mean and standard deviation (see chapters on variance and standard deviation) and then divide the standard deviation by the square root of the number of scores. He will report his finding as: $Mean= .......\pm....$
He will calculate the mean and standard deviation (see chapters on variance and standard deviation) and then divide the standard deviation by the square root of the number of scores. He will report his finding as: $Mean= .......\pm....$
The solution
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