Question I'm taking a Business Statistics course. I'm trying to understand the concept of standard deviation. My book uses the example of insurance companies to teach variance and standard deviation. In laymen terms, what exactly is standard deviation?
Thank you,
Davis
Answer davis -
your question is more properly addressed to the instructor of the course you are taking - or to
a ta, if there is one. you could also resort to dropping in on another faculty member that teaches stats and ask if they would be willing to spare some time to clarify the concept for you.
here is one example of what information a standard deviation [SD] conveys: the SAT exam scores range between 200 and 800 - with a mean score of 500 and a SD of 100. a person with a score of 600 on the exam is then 1 SD above the mean. since SAT scores have pretty much a [bell-shaped] normal distribution, this means that the score of 600 is at the 84th percentile: 84% of the examinees got 600 or less [and 16% got above 600].
usually scores are within 3 SDs of the mean - which means scores range from 200 [3 SDs below the mean] to 800 [3 SDs above] - as indicated above.
if some other exam also had a mean of 500 but a SD of 50, the score of 600 would be 2 SDs above the mean, and would then be at the 97.5th percentile - only 2.5% of examinees get above 600. the range of the scores for that exam would be from 350 to 650. the scores for this exam
vary less than for the SAT exam. so the SD is a measure of how much the scores vary. a small SD means scores do not vary much from individual to individual, while a large SD means individual scores can differ greatly from each other.
