How do you find the standard deviation for the population 9, 4, 6, 5, 4, 5, 5, 10?

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Answer 1 · 2017-03-05T18:44:38

#The S.D.~~2.12 (2dp),#

We have, the following #n=8# observations #x_i, 1 le i le 8 :#

#x_i : 9,4,6,5,4,5,5,10.#

#:. sum_(i=1)^(i=8) x_i=9+4+6+5+4+5+5+10=48.#

#rArr "the Mean "barx=(sumx_i)/n=48/8=6.#

Recall that, the Standard Deviation #sigma# is given by,

#sigma=sqrt{sum_(i=1)^(i=8) (x_i-barx)^2/n},# we proceed as below :-

#(x_i-barx)=(x_i-6) : 3, -2,0,-1,-2,-1,-1,4.#

#(x_i-barx)^2 : 9, 4, 0, 1, 4, 1, 1, 16.#

#:. sum(x_i-barx)^2=36.#

#rArr sigma=sqrt(36/8)=sqrt(9/2)=sqrt(4.5)~~2.12 (2dp).#