Question

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18. The point estimate of the population standard deviation isa. 2.000b. 1.291c. 1.414d. 1.667

Answer 1

Answer:( c ) 1.414

Explanation:

Let m be mean

M=mean=sum/n

M= (16+19+18+17+20+18) / 6

M=108/6

M=18

Let start finding:

The standard deviation formula is= sqrt( Summation of |x-m|^2 / n-1)

|x-m|^2

For 1st: |16-18|^2=4

For 2nd: |19-18|^2=1

For 3rd: |18-18|^2=0

For 4th: |17-18|^2=1

For 5th: |20-18|^2=4

For 6th: |18-18|^2=0

Summation of |x-m|^2 =10

The standard deviation formula is :

S.D = sqrt( Summation of |x-m|^2 / n-1)

S.D= sqrt(10 / 5)

S.D=sqrt(2)

S.D= 1.414