# Statistics Riddle

Discussion in 'Off-Topic' started by Cpt. Cynical, Sep 29, 2006.

1. ### Cpt. CynicalChieftain

Joined:
Jul 28, 2002
Messages:
11
My stats instructor gave the class an interesting statistical riddle today. Here's how it goes:

Calculate:

111,111,111 X 111,111,111

How is the answer like the normal curve (standard normal distribution)?

The answer, I think, is 12,345,678,987,654,321. How is that like the normal curve?

Well, I can figure out that the number obviously looks "bell-shaped" in that it starts with 1 on the outside and ascends to 9 in the middle.

Can you folks think of anything else? This is getting on my nerves, as if I am missing something obvious because I'm not savvy with statistics.

2. ### brennanArgumentative Brit

Joined:
May 12, 2005
Messages:
8,178
Location:
Worthing, Southern England
123...321 would just be a triangle

1x1=1
11x11=121
111x111=12321
1111x1111=1234321

Pattern established. Not a bell curve though.

Joined:
Apr 9, 2002
Messages:
49,076
Location:
Salisbury Plain
Brennan seems to be on the mark here.

I'm curious as to the origin of this riddle.

4. ### Brighteyeintuitively Bayesian

Joined:
Jan 19, 2006
Messages:
5,742
Location:
Oxford
You could also say that as you multiply larger 1111 numbers a bar graph of the result approximates ever more closely to a triangle, just like larger ns give a mean that approximates more closely to the normal distribution.
Yes, I know its tenuous.

Joined:
Apr 9, 2002
Messages:
49,076
Location:
Salisbury Plain
I wonder how the digit pattern changes under different bases. Someone mak me some graphs! I'd do it now, but it's 3:00 AM.

6. ### brennanArgumentative Brit

Joined:
May 12, 2005
Messages:
8,178
Location:
Worthing, Southern England
Binary:

1x1 = 1
11x11 = 1001
111x111 =110001
1111x1111 = 11100001
11111x11111 = (on my calculator it's E for error, but..) 1111000001
111111x111111 = 1111110000001

Odd pattern. Interesting though.

7. ### ElrohirRELATIONAL VALORIZATION

Joined:
Nov 22, 2004
Messages:
12,507
I think it's capital "E" for exponent.

8. ### brennanArgumentative Brit

Joined:
May 12, 2005
Messages:
8,178
Location:
Worthing, Southern England
Trust me man. I know what notation my scientific calculator uses for exponent. When all it does is say -E- it means the number is too big to show. (it doesn't show exponents in bases other than 10).

9. ### XenocratesChieftain

Joined:
Nov 25, 2005
Messages:
2,378
Location:
Liverpool
Is it possible, stat fans, that the OP's answer
should be interpreted 10^1, 10^2 etc?

I know that also wouldn't resemble a normal distribution as the top should flatten off, but at least it's curved......

Now this is driving me crazy too (a short drive Brennan ), how much like a normal curve should this be exactly?

10. ### nihilisticIntergalatic Delivery Boy

Joined:
Feb 24, 2003
Messages:
3,261
Location:
NNYC
Besies symmetry, it is not. That's the end.

There is nothing obvious besides the stupidity of the question. Likewise this question also has nothing to do with statistics and everything to do with numerology.

11. ### Red StrangerChieftain

Joined:
Aug 28, 2005
Messages:
1,678
It's like statistics because in the end it's just numbers. Anyone can try to make sense of the numbers or try to find patterns in the numbers. But it's just an illusion.