What makes the standard deviation approximated by the range rule of thumb much different from the standard deviation calculated directly from sample data? For example, if the approximate standard deviation is 15.36 and the standard deviation calculate from the sample set directly is 21. Is that possible that the way of collecting the data is not valid?
Suppose that the following data are test scores from one physics class in college. 26, 26, 39, 39, 42, 56, 65, 66, 76, 79, 80, 86, 87
The mean is 58.14, and the standard deviation is 20.94. However, by applying the range rule of thumb, I got 15.25. Why the difference is so large?
Also, in general, does college test scores satisfy normal distribution?
Thanks in advance