Question

A friend claims that education (years of school) is normally distributed. You believe she’s wrong. A reasonable argument for your point of view is that:

A. About 50% of individuals have greater than 12 years of schooling.
B. The standard deviation for years of schooling is less than the mean
C. Education has several modes (for example, at 12 and 16 years).
D. Education outcomes are uniformly distributed (all numbers of years are equally likely).
E. None of these are reasonable arguments.

Answer 1

@jim_thompson5910 @perl

Answer 2

does option a) seem plausible?

Answer 3

does 1 in 2 people go to college?

Answer 4

To be normally distributed, what must be true?

It must take on a bell curve, with one peak (how does that relate to the mode?). Also, does a uniform distribution look like a bell curve?

Answer 5

i didn't think so, i was thinking it was D. but was debating between that and C

Answer 6

I think those are both good arguments as to why it is not normally distributed.

Answer 7

education (years of school) is normally distributed

concentrate on that

Answer 8

That is, C and D.

Answer 9

@hockeychick23 why do you think that education is *uniformly* distributed? are people likely to leave education in any year (say first grade versus the end of 12th grade versus 16th grade)

Answer 10

I think we can assume that any option is true, and if one is true, then that must entail a non-normal distribution. If it does not entail such a thing, that would be an incorrect argument.

Answer 11

no i don't think the same amount of people would leave in 1st vs 12th @inkyvoyd

Answer 12

@hockeychick23 then would education be a *uniform* distribution?

Answer 13

hint:
12 years = high school diploma
16 years = bachelors degree

Answer 14

But, maybe you two are right -- part of the problem may be assessing whether an option is even plausible, not to mention if plausible, does that imply a non-normal distribution.

Answer 15

4 years = post-secondary education

Answer 16

2 more years for masters

Answer 17

the graph of years of schooling you should see spikes in 12 and 16 (and then 18 )

Answer 18

@perl oh i don't think the same amount of people would get a bachelors degree as 12th

Answer 19

Yes, so @hockeychick23 could your distribution be uniform if there are a different amoutn of people getting a bachelors degree versus just graduating high school?

Answer 20

no

Answer 21

Doesn't that eliminate your answer choice D?

Answer 22

yea, but then isnt it was unimodal so then it would also eliminate C also and i don't think A is right

Answer 23

What makes you think it is unimodal?

Answer 24

remember you are trying to dissuade someone that it is a normal distribution

Answer 25

you are trying to convince someone it is *not* a normal distribution

Answer 26

@perl oh so would that mean i could claim that there were more than one mode to get them to agree to my argument?

Answer 27

http://en.wikipedia.org/wiki/Educational_attainment_in_the_United_States#/media/File:Educational_Attainment_in_the_United_States_2009.png
50% vs 30% (have to subtract 80-30=50 since we are talking about people who JUST graduate from high school) seems pretty close

Answer 28

right, that is sufficient to exclude the possibility of it being a normal distribution. a normal distribution has one mode.

Answer 29

ok so saying education has several modes (i.e: 12 and 16) would be a reasonable argument

Answer 30

Well, wouldn't you say it's the only plausible one of the choices? :)

Answer 31

yes, and consider whether the other options could serve as reasonable arguments against years of schooling as normally distributed

Answer 32

ok thanks, i don't think the other options are very reasonable

Answer 33

ok thanks!!

Answer 34

Option D could serve as a reasonable argument *if* the scores were uniformly distributed in the first place. But scores are not uniformly distributed. Therefore we can't use it as a counterargument for it being normal.

Answer 35

:)