Hello, first time poster here, need some help with this homeworkquestion please!

Question

Hello, first time poster here, need some help with this homeworkquestion please!

Suppose that after computing xn(dash on the x, don't know how todo the syntax) based on n sample observations x1,...,xn,another observation xn+1 becomes available. (i) What is the relationship between the mean of the first nobservations, the new observation, and the mean of all n+1observations? (ii) For the strength observations givenbelow:

22.2    40.4   16.4    73.7   36.6    109.9    30.0  4.4        33.1  66.7   81.5,

Explanation / Answer

< Xn>= average of n observations = sum of nobservations/n

ð Sum of n observations = <xn> * n

ð Sum of n+1 observations = sum of n observations +Xn+1

ð sum of n+1 observations = <xn> * n+Xn+1

ð Average of n+1 observations = (<xn> * n+Xn+1)/(n+1)

ð <Xn+1> = (<xn> * n+Xn+1)/(n+1)

Using the same formula

Average of 11 observations = (43.34*10 +81.5)/11 =46.80909

Hope this helps you. Keep posting for any help.

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