amitdgr wrote:
[list]
11. SD ranks the dispersion (deviation) of the numbers in a list. The more alike the numbers are, the less the dispersion, so the less the standard deviation
13. The more uneven members are dispersed around their arithmetic average, the more their SD
21. For data with approximately the same mean, the greater the range, the greater the SD
26. For odd number of consecutive integers median = mean
Please add if i missed something.
In 11: this could be confusing. A set such as {0,0,0,0, 1000000, 1000000, 1000000, 1000000} contains numbers which are very much 'alike' but the set has a huge standard deviation: all of its elements are very far from the mean.
In 13: I'm not exactly sure what you're trying to say here.
In 21: This is not a mathematical rule; indeed it's very often untrue. The set S = {100, 50, 50, 50, 50, 50, 50, 50, 0} has the same mean as the set T = {99, 99, 99, 99, 99, 99, 1, 1, 1, 1, 1, 1}, and has a larger range. It has a much smaller standard deviation, however.
In 26. For any number of consecutive integers, median = mean. You can remove the word 'odd'. Indeed, in any arithmetic progression, the median = mean.