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Answer:
How do you calculate standard deviation without a data set?
You can calculate from other information.
For example, if you roll a standard die, you’re equally likely to get results 1, 2, 3, 4, 5 or 6. The mean result is 1+2+3+4+5+66=3.5 . The variance is 12+22+32+42+52+626−3.52=916−12.25≈2.9167 . Therefore the standard deviation is 2.9167−−−−−√=1.7078 .
Or suppose you know that the chance that a scratch-off lottery ticket returns some prize is 1 in 10. If you buy 900 tickets, on average you will get 90 that return some prize. The standard deviation of the number is 900×0.1×(1–0.1)−−−−−−−−−−−−−−−√=81−−√=9 .
In many other situations you can calculate standard deviation from the information you have. In other situations you can estimate a subjective standard deviation from what you don’t know. You might look at someone and guess their age at 35, with a subjective standard deviation of 4 years.