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Math 127B, Notes for lecture 9
Mrinal Raghupathi
Monday, February 14th, 2011
Administrivia
The topics to be discussed today is the sample average. The material is based on chapter 23.
Reminders
1. Read chapter 23.3 – 23.4 for Wednesday. There is an online quiz posted due by Wednesday
8 am.
2. Homework 5 is due Thursday, 2/17 in recitation.
3. There will be a quiz in recitation over chapter 22.
1 The average of draws from a box
We are going to extend our ideas about the accuracy of percentages to the situation in which our
box contains more than just 0s and 1s.
We begin with a theoretical example.
Example 1
. The box is
1
2
3
4
5
. The AVE of the box is 3 and the SD of the box is
q
2
2
+1
2
+0
2
+1
2
+2
2
5
= 1
.
414
≈
1
.
4.
Suppose that we make 100 draws from the box. The EV of the sum is given by number of draws
×
AVE of box = 100
×
3 = 300. The EV of the average of draws from the box is given by
EV of average of draws =
EV of sum
number of draws
=
300
100
= 3
.
Note that there is some cancellation and we get that the EV of the average of the draws is equal
to the average of the box.
Now for the Standard error. The SE of the sum is given by
√
number of draws
×
SD of the box =
10
×
1
.
4 = 14. The SE of the average of the draws is given by
SE of average of draws =
SE of the sum
number of draws
=
14
100
= 0
.
14
.
1
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View Full DocumentNote that the SE of the average is smaller than the SD of the box and that the SE decreases as the
number of draws goes up.
o
Now we reverse the process. We make draws from a box, and attempt to infer the average of
the box from the average of the draws.
Example 2
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 Spring '11
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 Math, Statistics

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