Voiceover:"For a senior project, Richard is researching
"how much money a college graduate can
"expect to earn based on his or her major.
"He finds the following interesting facts:
"Basketball superstar Michael Jordan was a
"geology major at the University of North Carolina.
"There were only three civil engineering majors
"from the University of Montana.
"They all took the exact same job
at the same company, earning the same salary.
"Of the 35 finance majors from Wesleyan University,
"32 got high-paying consulting jobs,
"and the other 3 were unemployed.
"For geology majors from the University of
"North Carolina the median income will likely be ..."
and we have some options here,
"less than, equal to or greater than the mean."
And then we have to answer the same questions ...
"For civil engineering majors from Montana,
the median income ..."
Well actually these are both about median.
"The median income will be ..."
and we compare it against the mean.
And then, "For finance majors from Wesleyan ..."
We're going to compare the median income to the mean.
So to visualize this a little bit more,
I've copied and pasted this exact same problem
onto my scratchpad, so here it is, I can now write on this.
So, let's think about each of these.
"For geology majors from UNC,
"the median income will likely be ..."
How will that compare to the mean?
Well what do they tell us about UNC?
They tell us that Michael Jordan was a geology major
at the University of North Carolina.
So what will the distribution
of salaries probably look like?
So if we're thinking about the University of
North Carolina, probably will look something like this.
And I'm going to do a very rough distribution
right over here and let's say that this would be
a salary of 0, and let's say that is a salary of, I don't know
Let me put a salary of 50K here, I'll do this in thousands.
Let's say this is 100 thousand right over here.
And then you have Michael Jordan who is,
actually I'll do a little gap here because he's so far up,
I don't know exactly what he was making
but it was definitely in the tens of millions
of dollars a year so Michael Jordan is
way, way, way, way, up here.
So if you were to make a histogram or a
plot of all of the salaries we could say,
Okay well you know maybe we have, if you put all
of the folks from geology majors at
University of North Carolina...
well there's probably, especially right when they graduated
there's probably you know, 1, 2, 3, I could keep doing it.
A bunch of people maybe making 50K maybe
some people making a little bit more, maybe some
people up here, maybe some people there.
Some people there, some people there.
Right there, maybe someone's making 100K.
Maybe it's a couple of people up there,
maybe someone isn't making anything,
maybe they weren't able to find a job.
And then of course you have Michael Jordan
up here making you know, 10 million dollars
or 20 million dollars or something like that.
So when you have a situation like this
where you have this outlier of Michael Jordan
it's going to put, one way I think about it
it kind of tugs on the mean, it wouldn't affect
the median because remember the median is
the middle value so it doesn't matter how high
this number is, you can make this a trillion dollars
it's not going to change what the middle value is.
The middle value is still going to be the same
middle value, you can move this anywhere around
in this range it's not going to change the median.
But the mean will change, if this becomes really, really
astronomically high it will distort the actual
mean here, actually could distort it a good bit.
So for geology majors from UNC the median income
is going to be lower than the mean because
Michael Jordan is pulling the mean up.
So let me fill that in.
"So for geology majors from UNC, the median
"will be less than the mean."
Now let's think about the other ones,
"For civil engineering majors from Montana,
"the median income will be" blank "the mean."
Well they tell us there were only three civil engineering
majors from the University of Montana.
They all took the exact same job at the same company
earning the same salary.
So let's say all 3 of them earn 50 thousand dollars.
Let's say that's their salary so you have
if you were to calculate the mean it would be
50 + 50 + 50 over 3 which of course is 50.
That would be the mean.
If you wanted the median you list the salaries in order
and then you take the middle one, well the middle one
is 50, so in this case the median is equal to the mean.
So let's fill that in, median is equal to the mean.
And then finally, wait let me go back to my scratchpad.
Whoops, let me go back to my scratchpad here.
"For finance majors from Wesleyan, the median income
will be," blank "the mean."
So let's think about this distribution here.
So here we have 35, out of the 35, 32 got high-paying
consulting jobs so let's say that they were making
six-figures so the distribution might look
something like this, this is 0 and this is let's say
this is 50K and let's say that this right over here
is 100 thousand dollars a years.
So 32 got high-paying consulting jobs,
so you might have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
23, 24, 25, 26, 27, 28, 29, 30, 31, 32.
So the distribution for the people who got the jobs
might look something like that but there were
3 people who are unemployed so let's say they
got no income, so you have 1, 2, 3.
So this is now, you have 3 outliers like the Michael
Jordan situation but instead of them being very high
they are very low so they're going to pull the mean
lower, they're not going to, if these were 0
or these were 50, or these were over here,
they're not going to affect the median.
The middle number is still going to be the same.
But they are going to pull down the mean.
So here I would say that the median income will
likely be higher, will likely be greater than the mean.
Because the mean is going to get pulled down
by these outliers, these three people not make anything.
So let's fill that out.
"For finance majors from Wesleyan, the median income
"will likely be greater than the mean."
Now let's check our answer, and we got it right.