Question

A population is listed as the following: 10 115 19 11. 12. 13. 14. 15. 16. Find μ =? Find Σ(x-μ)-? Find Σ(x-A)-? Find ΣΧ_? Find Σχ2-? Find σ-?

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Answer #1

Solution:

Given data :

Population list = 1,3,6,10,15,19

Now, we have to find out the :

11. Find the mu:

We know the ,

mu= mean

The formula for the Mean = ( sum of the all samples ) / (no.of samples )

= 1+3+6+10+15+19

= 54 / 6

= 9

  herefore Mean  mu = 9

12. Find the  sum ( X- mu ) :-

Now,  sum ( X- mu ) =  ( 1-9) + (3-9) + ( 6-9) + ( 10-9) + ( 15-9) +( 19-9)

= - 8 - 6 - 3 +1 + 6 + 10

= -17 + 17

   = 0

herefore   (X-μ) = 0

13. Find the sum ( X- mu )^{2} :-

Now, sum ( X- mu )^{2} = ( 1-9)^2 + (3-9)^2 + ( 6-9)^2 + ( 10-9)^2 + ( 15-9)^2 +( 19-9)^2

sum ( X- mu )^{2} =   (- 8)^2 + (- 6 )^2 + (- 3)^2 +( 1)^2 + ( 6 )^2 + (10 )^2

= 64+ 36+ 9+ 1+36+100

= 246

herefore   (X-μ)2-246

14. Find the sum x :-

Now, sum x = 1+3+6+10+15+19

= 54

herefore x = 54

15. Find the sum x^{2}:-

Now, sum x^{2}  = 1^2 +3^2 + 6^2 + 10^2 + 15^2 +1 9 ^2

= 1+ 9 + 36 +100+ 225+ 361

= 732

herefore  sum x^{2} =732

16. Find the sigma :-

We know, the formula for the sigma is

sigma  =  sqrt{rac{sum (x-mu )^{2}}{n-1}}

= sqrt{rac{( 1-9)^2 + (3-9)^2 + ( 6-9)^2 + ( 10-9)^2 + ( 15-9)^2 +( 19-9)^2}{20-1}}

= sqrt{rac{ (- 8)^2 + (- 6 )^2 + (- 3)^2 +( 1)^2 + ( 6 )^2 + (10 )^2 }{19}}

= 6436+9+136+ 100 19

=  246 19

  = V12.947

= 3.5981

herefore  sigma = 3.5981

  

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