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New session has begun in
math111e_Room1.
Tuesday, March 28, 2006
5:08pm
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*+**** Ann--Willem entered
math111e_Room1. Tuesday, March 28, 2006 5:08pm
*+**** Frances--Beasman
entered math111e_Room1. Tuesday, March 28, 2006 5:32pm
*-**** Frances--Beasman left
math111e_Room1. Tuesday, March 28, 2006 5:32pm
*+****
Sharon Merson>>How do you think you did on the
test Ann?
*+****
*-****
*+****
*+**** Frances--Beasman
entered math111e_Room1. Tuesday, March 28, 2006 5:47pm
*+**** Bill--Beck entered
math111e_Room1. Tuesday, March 28, 2006 5:51pm
Bill Beck>>Hi, Ann, Sharon M., Sharon C. and
Fran!
Sharon Cochran>>Hi
Sharon Merson>>Hi
Ann Willem>>hi
*-**** Ann--Willem left
math111e_Room1. Tuesday, March 28, 2006 5:52pm
Bill Beck>>How are things back in
Sharon Merson>>ok, it will be in the 70's this
weekend
Bill Beck>>Golf!
*+**** Ann--Willem entered
math111e_Room1. Tuesday, March 28, 2006 5:53pm
*+**** Carolyn--Isaac entered
math111e_Room1. Tuesday, March 28, 2006 5:53pm
Sharon Merson>>lol
Bill Beck>>Hi again, Ann!
Ann Willem>>opps
Ann Willem>>hi
Carolyn Isaac>>hi all
Sharon Merson>>hi
Bill Beck>>Hi, Carolyn!
Carolyn Isaac>>hi bill
Bill Beck>>Has everybody taken Test 2?
Sharon Merson>>yes
Carolyn Isaac>>yes
Sharon Cochran>>Yes
Bill Beck>>Piece of cake?
Sharon Merson>>no
Carolyn Isaac>>no
Sharon Cochran>>Bope
Sharon Cochran>>Nope
*+**** Lisa--Schloer entered
math111e_Room1. Tuesday, March 28, 2006 5:55pm
Bill Beck>>Hi, LIsa!
Ann Willem>>i hope it was
Lisa Schloer>>hi
*+**** Jaime--Bankowski
entered math111e_Room1. Tuesday, March 28, 2006 5:56pm
*+**** Jaime--Bankowski
entered math111e_Room1. Tuesday, March 28, 2006 5:56pm
*+**** Jaime--Bankowski
entered math111e_Room1. Tuesday, March 28, 2006 5:56pm
Bill Beck>>Hi, Jaime!
*-**** Jaime--Bankowski left
math111e_Room1. Tuesday, March 28, 2006 5:56pm
*-**** Jaime--Bankowski left
math111e_Room1. Tuesday, March 28, 2006 5:56pm
Jaime Bankowski>>hello all
Sharon Merson>>hello
Bill Beck>>The good news is you've taken the
two hardest tests!
Sharon Merson>>Thank God!
Bill Beck>>It's downhill from here!
Sharon Cochran>>That is good to know
Sharon Merson>>yes it is
Ann Willem>>well last weeks homework was
certainlly easier
Bill Beck>>Do you realize that this is our
9th class out of 14 classes?
Sharon Merson>>yup
Sharon Cochran>>Yes!
Bill Beck>>FLASH FLASH FLASH The answers to this week's practice problems
are on http://www.mathsoftware.com/walkthru.html
*+**** Nicole--Russell
entered math111e_Room1. Tuesday, March 28, 2006 5:59pm
Nicole Russell>>hi everyone
Bill Beck>>I messed up the week 9 lesson and
removed the answers to the practice problems so I posted them on my website.
Bill Beck>>Hi, Nicole!
Bill Beck>>According to my clock, it's time
to get started.
Bill Beck>>Let me know when you are on page
Walk18_p1, please.
Lisa Schloer>>there
Sharon Merson>>there
Sharon Cochran>>There
Carolyn Isaac>>there
Nicole Russell>>there
Ann Willem>>there
Bill Beck>>Last week we studied measures of
central tendency.
Bill Beck>>We were looking for a number we
could use to represent the data.
Jaime Bankowski>>here
Bill Beck>>This week we're going to study
Standard Deviation and Range.
Bill Beck>>These are numbers (statistics)
that we use to tell how tightly packed our data is.
Bill Beck>>Okay, let's go to page 2,please.
*+**** LaDonna--Parham
entered math111e_Room1. Tuesday, March 28, 2006 6:01pm
*+**** Cheryl--Bagley entered
math111e_Room1. Tuesday, March 28, 2006 6:01pm
Bill Beck>>Neat formula!
Bill Beck>>Hi, LaDonna and Cheryl!
LaDonna Parham>>hello
Cheryl Bagley>>hi
Bill Beck>>We are on page Walk18_p2.
*+**** Wendy--Riggin entered
math111e_Room1. Tuesday, March 28, 2006 6:02pm
Bill Beck>>Hi, Wendy! We are on page Walk18_p;2.
*+**** Elaine--Sfondiles
entered math111e_Room1. Tuesday, March 28, 2006 6:02pm
Bill Beck>>Hi, Elaine! We are on page Walk18_p2.
Elaine Sfondiles>>k thanks!
Wendy Riggin>>Hi Thanks
Elaine Sfondiles>>oh professor beck once the
chat is over can i speak with you?
Bill Beck>>Yes, Elaine.
Elaine Sfondiles>>thank you
Bill Beck>>Okay, let's look at that formula.
Nicole Russell>>so what number is xi? is it
the sum
Bill Beck>>Do you see (xi - xbar)?
Sharon Merson>>yes
Lisa Schloer>>yes
Elaine Sfondiles>>yes
Sharon Cochran>>Yes
Frances Beasman>>yep
Wendy Riggin>>yes
Ann Willem>>yes
Cheryl Bagley>>yes
Bill Beck>>What we're doing is determining
the "deviation from the mean."
Bill Beck>>What we'd like to do is determine
all of these deviations from the mean, then add them and find the "average
deviation from the mean."
Bill Beck>>Unfortunately, when we find all these
deviations from the mean it turns out that some are negative numbers and some
are positive numbers so the sum turns out to be equal to zero.
Bill Beck>>Hence the squared term.
Bill Beck>>What we do is square each of the
deviations from the mean - that makes all of them positive.
Bill Beck>>Then we add (that's what that
Greek letter Sigma tells us to do).
Bill Beck>>Then we divide by n-1
Bill Beck>>I'll get back to that later.
Bill Beck>>And lastly, we take the square
root of our answer.
Bill Beck>>So we squared them and the took
the square root so we're approximately back where we started - APPROXIMATELY.
Bill Beck>>It turns out that this number, s,
is called the standard deviation and it gives us a number (statistic) that we
can use when comparing the density of various sets of data.
Bill Beck>>Now, how about that n-1 in the
denominator.
Bill Beck>>If we wanted a "mean
deviation from the mean" we should be dividing by n
Bill Beck>>-But this semester we are going
to be studying samples of data and it turns out that if we divide by n-1 we get
a better estimate of the standard deviation of the population.
Bill Beck>>For example, the set of all students taking MATH 111 at CCBC
is our population and the students in my class would be a sample from this
population.
Elaine Sfondiles>>then what is the benefit of
dividing by n versus n-1?
Bill Beck>>The set of college students in
Maryland might be our population and the students attending Towson U would be a
sample space.
Bill Beck>>Okay?
Sharon Merson>>ok
Bill Beck>>Good question, Elaine.
Bill Beck>>Much better mathmeticians than I
could prove that when we divide by n-1 we get a better estimate of the
population standard deviation.
Bill Beck>>I accept their proof and pass it
along to my students as fact!
Elaine Sfondiles>>nice!
Bill Beck>>We'll use n-1 since we are using
a sample standard deviation to predict the population standard deviation.
Bill Beck>>Whew
Sharon Cochran>>My head is spinning
Sharon Merson>>mine too
Bill Beck>>If we were studying populations,
we'd divide by n
Bill Beck>>The good news is you just need to
use the formula.
Bill Beck>>Okay, let's go to page 3, please.
Elaine Sfondiles>>all these formulas are
confusing. the complements formulas really threw me for a loop
Nicole Russell>>There is a shorter way...
right?
Nicole Russell>>what happens when n=100, we
are not going to have to do that
Bill Beck>>Yes, Nicole, but we won't cover
it this semester. We're only going to
spend one night on standard deviation, so this is the only formula we'll cover.
Nicole Russell>>ok
Bill Beck>>None of our sample will be that
big, Nicole.
Nicole Russell>>ok
Bill Beck>>Okay, on page 3, we've subtracted
the mean from each of our scores in our sample.
Bill Beck>>We've got our deviations from the
mean.
Bill Beck>>Go to page 4,please.
Wendy Riggin>>why does n=5?
Bill Beck>>There are 5 items in our sample,
Wendy.
Wendy Riggin>>sorry!
Bill Beck>>Okay, go to page 5, please.
Bill Beck>>A little algebra.
Bill Beck>>Go to page 6, please.
Bill Beck>>Go to page 7, please.
Bill Beck>>Go to page 8, please.
Bill Beck>>So the standard deviation for
this sample space is approximately 2.24.
Bill Beck>>Let me remind you that a sample
space of size 5 is not really big enough to predict anything about the
population, but it's easier for us to use in a chat room.
Bill Beck>>Okay, let's go to the next
walkthru, please.
Wendy Riggin>>ok
Sharon Merson>>ok
Bill Beck>>Let me know when you are on page
Walk19_p1, please.
Sharon Merson>>there
Lisa Schloer>>there
Ann Willem>>ok
Sharon Cochran>>There
Nicole Russell>>ok
Carolyn Isaac>>ok
LaDonna Parham>>there
Cheryl Bagley>>there
Bill Beck>>OUr scores are 0, 1, 2, and 3.
Elaine Sfondiles>>k
Bill Beck>>The column headed by fi is the
frequencies of these scores.
Bill Beck>>Since we need to find x - xbar,
we must first determine the mean, xbar.
Bill Beck>>Go to page 2,please.
Bill Beck>>This is similar to last week's
lesson.
Bill Beck>>Go to page 3,please.
Bill Beck>>So there are 40 scores. This is a good sized sample.
Bill Beck>>Go to page 4, please.
Bill Beck>>THe sum of our scores is 75
Bill Beck>>Go to page 5, please.
Bill Beck>>I've rounded the mean off to
2-decimal places.
Bill Beck>>Now we need to determine the
deviations from the mean.
Bill Beck>>Go to page 6, please.
Bill Beck>>0-1.88 = -1.88
Bill Beck>>Don't forget the negative sign!
Bill Beck>>Go to page 7, please.
Bill Beck>>1 - 1.88 = -.88
Bill Beck>>Go to page 8, please.
Bill Beck>>Go to page 9, please.
Bill Beck>>These are our deviations from the
mean. Now we need to make these
deviations positive.
Bill Beck>>Go to page 10, please.
Bill Beck>>(-1.88)(-1.88) = 3.53
Bill Beck>>Okay?
Elaine Sfondiles>>...k
Sharon Cochran>>yes
Cheryl Bagley>>ok
Lisa Schloer>>k
Bill Beck>>Go to page 11, please.
Wendy Riggin>>yes
Carolyn Isaac>>ok
Bill Beck>>Go to page 12,please.
Bill Beck>>Go to page 13, please.
Jaime Bankowski>>are we rounding to a whole
number
Nicole Russell>>How do we get 3.53 again
Bill Beck>>No, we're going to round off to
2-decimal places.
Jaime Bankowski>>would we put 38.44 or just
38
Bill Beck>>(-1.88)(-1.88) = 3.53
Nicole Russell>>got it, sorry
Bill Beck>>Actually, we know that the
product of two negative numbers is positive, so we could just use (1.88)(1.88)
Bill Beck>>Okay, go to page 14, please.
Bill Beck>>Now we are going to take into
account that there are 6 of these deviations of size -1.88
Bill Beck>>Go to page 15, please.
Bill Beck>>And that there are 8 of these
deviations of size -.88
Bill Beck>>Go to page 16, please.
Bill Beck>>Go to page 17, please.
Bill Beck>>Now we're ready for our fomula.
Bill Beck>>formula
Bill Beck>>Go to page 18, please.
Bill Beck>>WE need to add those numbers.
Bill Beck>>Go to page 19, please.
Bill Beck>>Here's our "grouped
data" formula.
Jaime Bankowski>>how did we get the 46.20
Bill Beck>>We added 21.18+6.16+.11+18.75
Bill Beck>>That's what that Greek letter
Sigma tells us to do - add.
Jaime Bankowski>>i got a higher number
Bill Beck>>Go to page 20, please.
Bill Beck>>Plug and chug
Jaime Bankowski>>im getting 57.09
Jaime Bankowski>>oh .11
Jaime Bankowski>>haha
Bill Beck>>Go to page 21,please.
*-**** LaDonna--Parham left
math111e_Room1. Tuesday, March 28, 2006 6:32pm
Bill Beck>>So according to our calculations,
we predict that the standard deviation for the population is 1.09
Bill Beck>>With me?
Sharon Merson>>I get 1.18?
Nicole Russell>>yes
Sharon Cochran>>yep
Wendy Riggin>>yes
Elaine Sfondiles>>kinda
Cheryl Bagley>>1.18
Bill Beck>>Sharon, you need to take the
square root of 1.18
Bill Beck>>The square root of 1.18 is 1.09
Bill Beck>>Okay?
Cheryl Bagley>>got it
Frances Beasman>>okay here
*-**** Frances--Beasman left
math111e_Room1. Tuesday, March 28, 2006 6:34pm
Lisa Schloer>>yes
Sharon Cochran>>yes
Sharon Merson>>now I get it thanks
Elaine Sfondiles>>oh ok now i got it
Bill Beck>>On the test, I'll supply the
table and the formulas, you need to supply a calculator!
Sharon Cochran>>Good
Bill Beck>>Okay, let's go to the last
walkthru for tonight.
Elaine Sfondiles>>good
Wendy Riggin>>ok
Carolyn Isaac>>thereok
Sharon Merson>>there
Sharon Cochran>>there
Nicole Russell>>there
Lisa Schloer>>ok
Elaine Sfondiles>>k
Ann Willem>>ok
Bill Beck>>This is a very powerful theorem,
although it has very limited applications.
Bill Beck>>NOTE NOTE NOTE this theorem can
be appied only when k is greater than one.
Bill Beck>>If k = 1, you can't apply this
theorem.
Bill Beck>>If k is less than 1, you can't
apply this theorem.
Elaine Sfondiles>>what would you use it it was
one?
Bill Beck>>I'll bet a penny there's a
homework problem where this fact is important.
Bill Beck>>We don't have a theorem for that
case, Elaine.
Elaine Sfondiles>>ok
Sharon Merson>>ok
Bill Beck>>Okay, let's go to page 2, please.
Bill Beck>>Go to page 3, please.
Bill Beck>>Go to page 4,please.
Bill Beck>>Go to page 5, please.
Bill Beck>>Go to page 6, please.
Bill Beck>>Now let's look at a couple of
examples.
Bill Beck>>Suppose I have a distribution
with standard deviation 5
Bill Beck>>And let's suppose our mean is 8
Bill Beck>>8 + 2(5) = 8 +
10 =
18
Bill Beck>>8 - 2(5) = 8 -
10 =
-2
Bill Beck>>According to Chebyshev, 75% of
our scores will fall between -2 and 18
Bill Beck>>Okay?
Elaine Sfondiles>>k
Bill Beck>>He doesn't need to see your
scores. If the mean is 8 and the
standard deviation is 5, then he knows that 75% of the scores lie between -2
and 18
Bill Beck>>Let's look at one more example.
Nicole Russell>>little lost here... where did
the 2 come from
Bill Beck>>2 standard deviations from the
mean. k = 2
Bill Beck>>Okay?
Nicole Russell>>so i can put any number there
just as long it is more than 1
Bill Beck>>Yes.
Bill Beck>>And since we put in k=2, we're
going to work with that value of k.
Bill Beck>>Once again, Chebyshev says
"at least 75% of the scores will lie within 2 standard deviations of the
mean."
Nicole Russell>>ok
Bill Beck>>Now suppose s = 3 and xbar = 21
Bill Beck>>21 + 2(3) = 21 +
6 = 27
Bill Beck>>21 - 2(3) = 21 - 6 = 15
Nicole Russell>>got it
Bill Beck>>So Chebyshev says at least 75% of
the scores will lie between 15 and 27.
Bill Beck>>And he has never seen your
scores!
Bill Beck>>Clever fellow.
Bill Beck>>Okay, let's go to page 7, please.
Bill Beck>>Go to page 8, please.
Bill Beck>>A picture is worth a thousand
words.
Bill Beck>>Go to page 9, please.
Bill Beck>>Go to page 10, please.
Bill Beck>>The mean is 30 and both 20 and 40
are 10 units from the mean.
Bill Beck>>Our next question is, "how
many standard deviations is 10"?
Bill Beck>>In other words, if one standard
deviation is 4, how many standard deviations is 10?
Bill Beck>>Go to page 11,please.
Bill Beck>>With me?
Nicole Russell>>yes
Elaine Sfondiles>>yes
Wendy Riggin>>sure
Ann Willem>>ok
Bill Beck>>Okay, let's go to page 12,please.
Bill Beck>>Go to page 13,please.
Bill Beck>>Go to page 14,please.
Bill Beck>>Go to page 15,please.
Bill Beck>>Go to page 17, please.
Bill Beck>>So 84% of the scores lie between
20 and 40
Bill Beck>>Without seeing any of the scores!
Bill Beck>>Okay, Class, this might take a
little time to sink in.
Bill Beck>>Any questions?
Sharon Merson>>yeah
Elaine Sfondiles>>none i can think of right
now
Nicole Russell>>yes
Sharon Merson>>nope
Lisa Schloer>>not yet
Sharon Cochran>>I need to think about it
Bill Beck>>Shoot
Carolyn Isaac>>no
Bill Beck>>What's your question, Sharon M.?
Nicole Russell>>How do you find the range in
first example
Sharon Merson>>yeah to the time to sink in
Bill Beck>>The range is the difference
between the biggest score and the smallest score.
Ann Willem>>What is a real life application
of this lesson today
Bill Beck>>Do you have a question, Nicole?
Sharon Merson>>I like range...it's easy
Nicole Russell>>thanks, you answered it
Bill Beck>>When you read professional
journals in your field, you'll find applications of standard deviation.
Bill Beck>>Sociology, nursing, etc.
Ann Willem>>is it like room for error
Bill Beck>>I don't understand your question,
Ann.
Ann Willem>>i am not sure i can explain it
either
Bill Beck>>I guess you could loosely think
of standard deviation as "plus minus error."
Sharon Merson>>Ann, I think it's like is the
average accurate
Bill Beck>>Very loosely, Ann.
Ann Willem>>ok thats what i meant
Bill Beck>>Now I understand, Ann.
Nicole Russell>>Mr. beck any way I can speak to
you
Bill Beck>>Okay, Class, that's it for
tonight.
Bill Beck>>Any questions?
Sharon Merson>>Thanks
Sharon Cochran>>Bye
*-**** Sharon--Cochran left
math111e_Room1. Tuesday, March 28, 2006 6:56pm
Bill Beck>>G'night
Sharon Merson>>nite
*-**** Sharon--Merson left
math111e_Room1. Tuesday, March 28, 2006 6:56pm
Lisa Schloer>>good night all
*-**** Jaime--Bankowski left
math111e_Room1. Tuesday, March 28, 2006 6:56pm
Wendy Riggin>>Thanks Bill Goodnight
Cheryl Bagley>>good nite
*-**** Wendy--Riggin left
math111e_Room1. Tuesday, March 28, 2006 6:56pm
*-**** Lisa--Schloer left
math111e_Room1. Tuesday, March 28, 2006 6:56pm
Carolyn Isaac>>G'night, until next week
*-**** Carolyn--Isaac left
math111e_Room1. Tuesday, March 28, 2006 6:57pm
Bill Beck>>Okay, Class, G'night!
Ann Willem>>nite
*-**** Ann--Willem left
math111e_Room1. Tuesday, March 28, 2006 6:58pm
*-**** Bill--Beck left
math111e_Room1. Tuesday, March 28, 2006 6:58pm
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math111e_Room1. Tuesday, March 28, 2006 6:58pm
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math111e_Room1. Tuesday, March 28, 2006 6:58pm
*-**** Cheryl--Bagley left
math111e_Room1. Tuesday, March 28, 2006 7:04pm
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Tuesday, March 28, 2006
7:04pm
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New session has begun in
math111e_Room1.
Tuesday, March 28, 2006
8:12pm
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*+**** Lucretia--Thomas
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Tuesday, March 28, 2006
8:12pm
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