When should we need to be concerned regarding the characteristics of the probability distribution of the sample means?

Question

Should we need to be concerned regarding the characteristics (i.e. maybe being non-normal) of the probability distribution of the sample means in a situation where we have 51 data points with sample mean 5.25 and sample variance 11?

Select one:
A: Yes
B: No

Answer 1

In the sample the statistics summary describes the data in terms of the mean and standard deviation (SD). In this case the sample SD=√11=3.32 approx. and the summary is 5.25±3.32. This means that the 51 data values tend to be between 1.93 and 8.57. Nothing to be concerned about, so I think the answer is B: No.

Comments

Hello Rod, thank you for your help as always.