This is very possibly not the best place to ask this, however it's the best I could find but please suggest anywhere else that might be better suited.

I'm building a sort of challenge revolving around doing simple mental arithmetic (numbers between 1 - 100 using division, multiplication, addition and subtraction) in a set time period and grading based on number of correct answers in given period.

In order to establish a baseline I'm looking for some information regarding how many correct mental arithmetic problems people can solve in, for example, 2 minutes. Ideally I'm trying to find the bell curve information on this (the lowest, average and best).

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    $\begingroup$ Since you are asking for statistics on this, maybe Cross Validated would be nice? Keep this here, and make another post there. $\endgroup$ – Guy Mar 18 '14 at 19:23
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    $\begingroup$ He/she may be a "competitor", but you might try to contact the person behind this. $\endgroup$ – Daniel R Mar 18 '14 at 19:29
  • $\begingroup$ Maybe cogsci.stackexchange.com is a better place to ask this... $\endgroup$ – draks ... Mar 19 '14 at 21:57

There are people which they have different mental abilities to functionally produce answers to these mental arithmetic questions in under 2 minutes. Hence that the time will change depending on the mental abilities of the people in question.

I hope this answered your question.

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    $\begingroup$ This is my point exactly. People do have radically different abilities which is why I'm trying to work out a bell-curve to use as the marking scale. With a maths genius on one end and a two year old child at the other end. Assuming a standard two year old child just learning basic maths. $\endgroup$ – Flatlyn Mar 18 '14 at 21:25

Here's an initial sketch of what I would do:

People are too lazy for this. So, do it in reverse. Ahhhmm.

In a Web application ("Are you smarter ?"), give users two abilities:

  1. Take the test. (Largest weight on information gathered this way).
  2. Browse through tests other "users" took, and show only the questions, the score/grade, and maybe the time it took to finish.

With this, let the users (You choose one or more of these, and think of more):

  1. Rank the "smartness" (significant weight, with the option to disregard at a later time)
  2. Assert that they are smarter, i.e these are not so good test results (Minor weight, with the option to disregard at a later time). This would direct them to the beginning of a "similar" test (Large weight on this).
  3. Give the explicit option to take "this" test ("Similar") (Large weight on this).

In actual tests you should gather as much information as you can, i.e, etc..

This is a feedback loop, initialized with fabricated users, tests, and results.

Gradually/Slowly, it would/should:
1. Be able to generate better tests (Better means many things here), e.g like choosing the best book to learn a given subject.
2. Make "Similar" test really more and more similar.
3. Make the statistics closer and closer to the objective unknown you are actually after, either by real empirical data, a clever summary of subjective data, or (Most probably) a clever combination of these...

  • $\begingroup$ I really wish I could mark this answer as correct as you have excellent suggestions but it doesn't really answer my question. The issue is at the moment the challenge is non-networked, meaning there is no plan to have backend databases collecting and processing all that data. That being said it's an excellent idea for further development. $\endgroup$ – Flatlyn Mar 18 '14 at 21:27
  • $\begingroup$ @JamesKraw note that there does not exist a question mark in your question, both literally and not.. :-). (What exactly is the question..?) :-) You can draw an exact curve right in this instant. But if you want to learn something of significance from it, you need a lot of data behind it.. $\endgroup$ – user76568 Mar 18 '14 at 21:48

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