What is the best approximation of the standard deviation of #{10,15,20,25,30}# - #5,7.5# or #10#?

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Answer 1 · 2016-09-23T15:04:15

Standard deviation can be best approximated by #7.5#.

The mean of #{10,15,20,25,30}# is

#(10+15+20+25+30)/5=100/5=20#.

The deviations from mean are #{-10,-5,0,5,10}# and

square of deviations are #{100,25.0,25,100}# and

average deviation is #{100+25+0+25+100)/5=50#

and standard deviation is #sqrt50=7.071#

Hence, standard deviation can be best approximated by #7.5#.