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Standard deviation of 300, 785, 670, 187, 760, 724

Answer :

STEP 1

Mean = [tex] \frac{300+785+670+187+760+724}{6} = \frac{3426}{6}=571 [/tex]

STEP 2

Subtract the mean from each data value then square the answer
[tex]300-571=-271[/tex] ⇒ [tex] (-271)^{2} =73441[/tex]
[tex]785-571=214[/tex] ⇒ [tex] (214)^{2}=45796 [/tex]
[tex]670-571=99[/tex] ⇒ [tex] (99)^{2}=9801 [/tex]
[tex]187-571=-384[/tex] ⇒ [tex] (-384)^{2} =147456[/tex]
[tex]760-571=189[/tex] ⇒ [tex]189^{2}=35721 [/tex]
[tex]724-571=153[/tex] ⇒ [tex]153^{2} =23409[/tex]

STEP 3

Add the squared answers in STEP 2 then find the mean

[tex] \frac{73441+45796+9801+147456+35721+23409}{6}= \frac{335624}{6}=55937.3 [/tex]

STEP 4

Square root the answer in STEP 3
[tex] \sqrt{55937.3} =236.5[/tex]

Standard deviation is 236.5

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