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Fwd: FlowingData - Best statistics question ever

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Victoria Hughes

Fwd: FlowingData - Best statistics question ever

Best statistics question ever
Posted: 28 Oct 2011 01:25 AM PDT

$Best Math Question EVAR$
By way of Raymond Johnson, the best statistics multiple choice question ever written on a chalkboard. Try not to think too hard. [via]

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Owen Densmore

Re: [sfx: Discuss] Fwd: FlowingData - Best statistics question ever

Administrator

On Sat, Oct 29, 2011 at 9:12 AM, Tyler White <[hidden email]> wrote:

The solution depends on how you consider the answers... you can say that there are four unique answers (A, B, C, D) or you could say there are only 3 answers (25%, 50%, 60%). It's a trick question! Hahahah....

Tyler White¹
http://TylerWhiteDesign.com
http://twitter.com/Uberousful

On Oct 29, 2011, at 11:27 AM, Victoria Hughes wrote:

Best statistics question ever

Posted: 28 Oct 2011 01:25 AM PDT

By way of Raymond Johnson, the best statistics multiple choice question ever written on a chalkboard. Try not to think too hard. [via]

You are subscribed to email updates from FlowingData
To stop receiving these emails, you may unsubscribe now. Email delivery powered by Google

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Owen Densmore

Re: [sfx: Discuss] Fwd: FlowingData - Best statistics question ever

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Oops fat fingered earlier email. I think this, as Tyler sez, is tricky because of the double 25. You have a 50% chance of 25, but only 25% of the other two. Like the Monty Hall, I'd like to hear a pro reason through to the answer.

On Sat, Oct 29, 2011 at 9:39 AM, Owen Densmore <[hidden email]> wrote:

On Sat, Oct 29, 2011 at 9:12 AM, Tyler White <[hidden email]> wrote:

The solution depends on how you consider the answers... you can say that there are four unique answers (A, B, C, D) or you could say there are only 3 answers (25%, 50%, 60%). It's a trick question! Hahahah....

Tyler White¹
http://TylerWhiteDesign.com
http://twitter.com/Uberousful

Carl Tollander

Re: [sfx: Discuss] Fwd: FlowingData - Best statistics question ever

Imagine it's not multiple choice...

On 10/29/11 9:44 AM, Owen Densmore wrote:

Oops fat fingered earlier email. I think this, as Tyler sez, is tricky because of the double 25. You have a 50% chance of 25, but only 25% of the other two. Like the Monty Hall, I'd like to hear a pro reason through to the answer.

On Sat, Oct 29, 2011 at 9:39 AM, Owen Densmore <[hidden email]> wrote:

On Sat, Oct 29, 2011 at 9:12 AM, Tyler White <[hidden email]> wrote:

The solution depends on how you consider the answers... you can say that there are four unique answers (A, B, C, D) or you could say there are only 3 answers (25%, 50%, 60%). It's a trick question! Hahahah....

Tyler White¹

http://TylerWhiteDesign.com

http://twitter.com/Uberousful
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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John Kennison

Re: [sfx: Discuss] Fwd: FlowingData - Best statistics question ever

Self-referential statements can lead to paradoxes, so one could say the question is not well-formed because it is self-referential.

If, as mentioned, choice (C) were 0%, and options (A),(B),(D) were unchanged, then the question leads to a paradox.

If choice (D) were 50%, and options (A), (B), (C) were unchanged, then both 25% and 50% would be consistent answers --so (A), (B) and (D) would all be defensible (but, obviously, they cannot all be correct).

As it stands the answer appears to be 0% since every choice leads to a contradiction, but I would prefer the answer that the question is not well-formed.
________________________________________
From: [hidden email] [[hidden email]] On Behalf Of Carl Tollander [[hidden email]]
Sent: Saturday, October 29, 2011 12:08 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] [sfx: Discuss] Fwd: FlowingData - Best statistics question ever

Imagine it's not multiple choice...

On 10/29/11 9:44 AM, Owen Densmore wrote:
Oops fat fingered earlier email. I think this, as Tyler sez, is tricky because of the double 25. You have a 50% chance of 25, but only 25% of the other two. Like the Monty Hall, I'd like to hear a pro reason through to the answer.

On Sat, Oct 29, 2011 at 9:39 AM, Owen Densmore <[hidden email]<mailto:[hidden email]>> wrote:

On Sat, Oct 29, 2011 at 9:12 AM, Tyler White <[hidden email]<mailto:[hidden email]>> wrote:
The solution depends on how you consider the answers... you can say that there are four unique answers (A, B, C, D) or you could say there are only 3 answers (25%, 50%, 60%). It's a trick question! Hahahah....

Tyler White¹
http://TylerWhiteDesign.com
http://twitter.com/Uberousful

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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Russell Standish

Re: Fwd: FlowingData - Best statistics question ever

In reply to this post by Victoria Hughes

What was the question?

On Sat, Oct 29, 2011 at 08:27:35AM -0600, Victoria Hughes wrote:

> >Best statistics question ever
> >Posted: 28 Oct 2011 01:25 AM PDT
> >
> >
> >By way of Raymond Johnson, the best statistics multiple choice
> >question ever written on a chalkboard. Try not to think too hard.
> >[via]
> >
> >
> >You are subscribed to email updates from FlowingData
> >To stop receiving these emails, you may unsubscribe now. Email
> >delivery powered by Google
> >Google Inc., 20 West Kinzie, Chicago IL USA 60610
>

> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

--

----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [hidden email]
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------

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Russ Abbott

Re: Fwd: FlowingData - Best statistics question ever

For Russ Standish, the question is here. And here's my plodding answer.

If 25% were the correct answer, then either (a) or (d) would be right. So one would have a 50% chance of getting the correct answer. Hence 25% is not the correct answer.

If 50% were the correct answer, then (b) would be right. But then one would have only a 25% chance of picking it by chance. So 50% is not the correct answer.

If one allowed either 25% or 50% as the correct answer, then 75% would be the correct answer since (a), (b), or (d) would be correct.

The joke should be that (c) reads 75% rather than 60%. In that case (d) would be the correct answer. Hence any answer would be correct and one would have a 100% chance of getting the correct answer.

But none of the answers is 100%. So the correct answer is 0%.

If as John suggests (d) were 0%, then if we decide that neither 25% nor 50% is the correct answer. then (d) is the correct answer. But in that case, one would have a 25% chance of getting the correct answer, etc.

On the other hand, the above could be taken to show that none of the suggested answers is correct. With (c) at 60%, that seems to be a reasonable conclusion. So pick any answer and one will be certain to be wrong. But since none of the answers offers that probability, any selection will be consistent with that result. Of course there is no way to select that answer from the ones given. But if there were, as we saw when we allowed (d) to be 0%, that would foul that answer up anyway.

-- Russ

On Sat, Oct 29, 2011 at 2:30 PM, Russell Standish <[hidden email]> wrote:

What was the question?

On Sat, Oct 29, 2011 at 08:27:35AM -0600, Victoria Hughes wrote:
> >Best statistics question ever
> >Posted: 28 Oct 2011 01:25 AM PDT
> >
> >
> >By way of Raymond Johnson, the best statistics multiple choice
> >question ever written on a chalkboard. Try not to think too hard.
> >[via]
> >
> >
> >You are subscribed to email updates from FlowingData
> >To stop receiving these emails, you may unsubscribe now. Email
> >delivery powered by Google
> >Google Inc., 20 West Kinzie, Chicago IL USA 60610

>

> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

--

----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [hidden email]
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------

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Robert J. Cordingley

Re: Fwd: FlowingData - Best statistics question ever

In reply to this post by Victoria Hughes

Here's how I'd analyze/state it.

It all revolves around the first 'if' statement. If I choose an answer at random then I can't let any information from that answer influence my result or it wont be random. Since there are 4 choices and now I can't pay attention to what they are, then at random each has an equal probability. A 25% B 25% C 25% D 25%. So given enough tries that's how the results would distribute. But two of the answers are the same so I have a 50% chance of choosing the answer represented by A or D which are clearly now the wrong answer - they don't match. I have a 25% chance of choosing B which also doesn't match and C doesn't match anything. So the chance of being correct is 0%.

Robert C

On 10/29/11 8:27 AM, Victoria Hughes wrote:

Best statistics question ever

Posted: 28 Oct 2011 01:25 AM PDT

$Best Math Question EVAR$

By way of Raymond Johnson, the best statistics multiple choice question ever written on a chalkboard. Try not to think too hard. [via]

You are subscribed to email updates from FlowingData
To stop receiving these emails, you may unsubscribe now. Email delivery powered by Google

Google Inc., 20 West Kinzie, Chicago IL USA 60610
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Owen Densmore

Re: [sfx: Discuss] Fwd: FlowingData - Best statistics question ever

Administrator

In reply to this post by Owen Densmore

If we take this seriously, which I doubt we should :), I think you'd have to create a tree of probabilities much like monty hall problem. (at least if there isn't a trivial nifty solution!)

So start at the root of the tree, generate a branch for choosing each of the three answers, 33.3% each.

Then place three branches at each for choosing that branch: 50% for 25%, and 25% for 50% and 60%. OK, 9 branches.

Now go through and add up all the probabilities that represent a right path. So for example, take 25% as the first branch, and look for the 25% in the second branch. Ditto for the other 2 possible paths.

This route gives 33.3% as the solution. Hmm..

The other approach is to simply say a, b, c, d are the choices which gives the 25%

Naturally the last approach is to say its a trick, or word game, or very subtle problem statement.

On Sat, Oct 29, 2011 at 9:44 AM, Owen Densmore <[hidden email]> wrote:

Oops fat fingered earlier email. I think this, as Tyler sez, is tricky because of the double 25. You have a 50% chance of 25, but only 25% of the other two. Like the Monty Hall, I'd like to hear a pro reason through to the answer.

On Sat, Oct 29, 2011 at 9:39 AM, Owen Densmore <[hidden email]> wrote:

On Sat, Oct 29, 2011 at 9:12 AM, Tyler White <[hidden email]> wrote:

The solution depends on how you consider the answers... you can say that there are four unique answers (A, B, C, D) or you could say there are only 3 answers (25%, 50%, 60%). It's a trick question! Hahahah....

Tyler White¹
http://TylerWhiteDesign.com
http://twitter.com/Uberousful