- #1

jwxie

- 282

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## Homework Statement

The book states the following:

The sample mean is defined by: [tex]\bar{x}=\sum_{i=1}^{n}x_{i}/n[/tex]

The computation of the sample mean can often be simplified by noting that if for constants

a and b, [tex]y_{i}=ax_{i}+b[/tex], then the sample mean of the data set y1 , . . . , yn is: [tex]\bar{y}=\sum_{i=1}^{n}(ax_{i}+b)/n=\sum_{i=1}^{n}ax_{i}/n+\sum_{i=1}^{n}b/n=a\bar{x}+b[/tex]

Given the question:

Given the question:

The winning scores in the U.S. Masters golf tournament in the years from

1982 to 1991 were as follows: 284, 280, 277, 282, 279, 285, 281, 283, 278, 277

The book computes as follows:

(1) Why are we choosing 280?? What is the reason for that? I tried other numbers don't they don't give the same sample mean.Rather than directly adding these values, it is easier to first subtract 280 from

each one to obtain the new valuesyi = xi − 280, we obtain:

4, 0, −3, 2, −1, 5, 1, 3, −2, −3

ecause the arithmetic average of the transformed data set is

y_bar = 6/10

̄

it follows that

x_bar = y_bar + 280 = 280.6

(2) I also want to confirm my understanding of the linear relation given the summation. I know the constant a should be the 1/n, as x1 / n + x2 / n + xn / n is the same as (x1+x2+xn)/n. Why do we need the b, the intercept? Is it just stating the obvious ,a general form? Or is it possible that we will encounter a statistical sample mean that cross the y?

But what I just said don't make sense to "yi = xi − 280". the constant a is 1...Can someone correct me? Thanks!