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

Question

3575 views around the world

You can reuse this answer
Creative Commons License

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).#