Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
03-21-2017, 03:43 PM (This post was last modified: 03-22-2017 03:24 PM by Vtile.)
Post: #1
 Vtile Senior Member Posts: 406 Joined: Oct 2015
Article - 42.86% responded “Yes” on an opinion poll. How many people responded?

Quote:0.4286 Enter XQ Enter

sry. I couldn't resist. The article is a good read.

Thank you.

The Joe Horns article is on article section of the forums with real answers.
03-21-2017, 11:51 PM
Post: #2
 Joe Horn Senior Member Posts: 1,825 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-21-2017 03:43 PM)Vtile Wrote:  The answer is

Quote:0.4286 Enter XQ Enter

sry. I couldn't resist. The article is a good read.

Thank you.

The Joe Horns article is on article section of the forums with real answers.

When I type 0.4286 XQ on my 50g I get 2143/5000, which is not the answer sought by the article. Perhaps you have your machine in 2FIX or 4FIX mode? I keep mine in STD mode. Regardless, the XQ function only uses the simple continued fraction algorithm, which fails to obtain the best solution much of the time, as explained in the PDQ Algorithm posting.

<0|ɸ|0>
-Joe-
03-22-2017, 09:19 AM
Post: #3
 eried Senior Member Posts: 744 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
I think the question is wrong, it should be "What is the minimum people who responded?"

Yes: 3
No: 4

From 7 people, 42.85714286% of the people answered Yes.

My website: erwin.ried.cl
03-22-2017, 11:56 AM (This post was last modified: 03-22-2017 11:57 AM by Joe Horn.)
Post: #4
 Joe Horn Senior Member Posts: 1,825 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-22-2017 09:19 AM)eried Wrote:  I think the question is wrong, it should be "What is the minimum people who responded?"

That's exactly the point that Chapter 3 of the article makes. It starts off explaining how most people ASSUME that more people were polled than necessary, and then the 3rd paragraph says, "So the question becomes: What is the smallest number of respondents which can make such a ratio possible?" The article thus points out the necessity of changing the assumed question into the more accurate question. So, as you can see, the article agrees with you.

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-Joe-
03-22-2017, 01:12 PM
Post: #5
 eried Senior Member Posts: 744 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-22-2017 11:56 AM)Joe Horn Wrote:  That's exactly the point that Chapter 3 of the article makes. It starts off explaining how most people ASSUME that more people were polled than necessary, and then the 3rd paragraph says, "So the question becomes: What is the smallest number of respondents which can make such a ratio possible?" The article thus points out the necessity of changing the assumed question into the more accurate question. So, as you can see, the article agrees with you.

Ups, sorry! I checked the pdf in the phone without much care. I thought this question was not answered in that article

My website: erwin.ried.cl
03-22-2017, 01:49 PM
Post: #6
 Vtile Senior Member Posts: 406 Joined: Oct 2015
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
^^ That is the reason of the bold note to look the real answer from the article..

@Joe, yes I use 4 decimal engineering notation. It happens to give the answer you end up with arguments in the article.

03-22-2017, 02:40 PM
Post: #7
 eried Senior Member Posts: 744 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-22-2017 01:49 PM)Vtile Wrote:  ^^ That is the reason of the bold note to look the real answer from the article..

@Joe, yes I use 4 decimal engineering notation. It happens to give the answer you end up with arguments in the article.

Yes, I see that now. I was just eager for any challenge, I guess

What if, 30.10335917% responded "Yes" on an opinion poll. How many people responded?

My website: erwin.ried.cl
03-22-2017, 02:51 PM
Post: #8
 Joe Horn Senior Member Posts: 1,825 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-22-2017 02:40 PM)eried Wrote:  What if, 30.10335917% responded "Yes" on an opinion poll. How many people responded?

Minimum: 233 out of 774. Maximum: currently approximately 2254741602 out of 7.49 billion.

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-Joe-
03-22-2017, 02:56 PM
Post: #9
 eried Senior Member Posts: 744 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-22-2017 02:51 PM)Joe Horn Wrote:
(03-22-2017 02:40 PM)eried Wrote:  What if, 30.10335917% responded "Yes" on an opinion poll. How many people responded?

Minimum: 233 out of 774. Maximum: currently approximately 2254741602 out of 7.49 billion.

hahaha! correct

My website: erwin.ried.cl
03-22-2017, 03:15 PM (This post was last modified: 03-22-2017 03:17 PM by Vtile.)
Post: #10
 Vtile Senior Member Posts: 406 Joined: Oct 2015
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
..And the silly fools method.
Code:
 .3010335917 7 ENG  Enter XQ  Enter
03-22-2017, 03:40 PM (This post was last modified: 03-22-2017 04:21 PM by Joe Horn.)
Post: #11
 Joe Horn Senior Member Posts: 1,825 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-22-2017 03:15 PM)Vtile Wrote:  ..And the silly fools method.
Code:
 .3010335917 7 ENG  Enter XQ  Enter

Yep, XQ even works for this example in STD mode! Ok, so my next quest is for an example that works as shown in the article and FAILS for XQ (and →Q) in EVERY display setting....

AHA! I think I found one: 71.45%. The simplest ratio that rounds to 71.45% is 388/543, but that's not returned by XQ or →Q in any display setting. So there.

Here's how to work it out using the article's method:
0.71445 = {0, 1, 2, 1, 1, 123, 1, 1, 1, 7} (continued fraction)
0.71455 = {0, 1, 2, 1, 1, 76, 1, 1, 1, 5, 2}
Truncated where they begin to differ plus 1 =
{0, 1, 2, 1, 1, 77} = 388/543

Or, using PDQ: 0.7145 0.00005 PDQ --> 388/543.

EDIT: Wow, there are many such examples. Try 10.1%. Or even 1%. Golly.

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-Joe-
03-23-2017, 09:02 AM (This post was last modified: 03-24-2017 09:32 AM by pier4r.)
Post: #12
 pier4r Senior Member Posts: 2,077 Joined: Nov 2014
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
Oh that's interesting. Thanks for the contribution!

I don't have the prime, does someone has the program for the 50g? Although XQ should be there.

Then an extension of the question: one has the percentage of Yes but also the number of yes over the no.

So one has:

yes / ( yes + no )

and

yes - no = number

How many yes and no are required for this?
This is a common case in sites with like/dislike. For example reddit: https://www.reddit.com/r/math/search?q=s...rict_sr=on

Taking one result at random:

Now reddit masks a bit the votes at every refresh(but not the ratio of likes/dislikes), but nevertheless one can try.

Yes - no = 62
Yes% = 94

How many 'yes', how many 'no'? (minimum of course)

The numeric solver on the hp 50 g returns (I translated in fraction) yes 1457/22 and no 93/22 . It may be not possible to get integers that solve the system above, maybe due to the reddit masking of numbers.

Wikis are great, Contribute :)
03-24-2017, 06:40 AM
Post: #13
 Joe Horn Senior Member Posts: 1,825 Joined: Dec 2013
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-23-2017 09:02 AM)pier4r Wrote:  I don't have the prime, does someone has the program for the 50g?

If you are referring to PDQ, it's here (read PDQ.TXT first): http://holyjoe.net/hp/PDQ.zip

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-Joe-
03-24-2017, 09:32 AM
Post: #14
 pier4r Senior Member Posts: 2,077 Joined: Nov 2014
RE: Article - 42.86% responded “Yes” on an opinion poll. How many people responded?
(03-24-2017 06:40 AM)Joe Horn Wrote:  If you are referring to PDQ, it's here (read PDQ.TXT first): http://holyjoe.net/hp/PDQ.zip

Many thanks, why do you not share it in the software library or on hpcalc.org ? Already the readme is way better than many other programs.

Wikis are great, Contribute :)
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