# Chebyshev's theorem (statistics)

1. Sep 20, 2008

### staples82

1. The problem statement, all variables and given/known data
If 100 students take a quiz, use chebyshev's theorem to predict the number of students plus and minus 2 standard deviations from the mean.

2. Relevant equations
1-1/k^2 where k is standard deviations

3. The attempt at a solution
I think its 75, but I'm not sure...I'm just trying to get this concept down

2. Sep 20, 2008

### HallsofIvy

Staff Emeritus
Don't just memorize formulas, learn what they say! Did you notice that "1- 1/k2" is not even an equation? What is equal to 1- 1/k2?

1- 1/22= 1- 1/4= 3/4. 3/4 of 100= 75. Now, if "the fraction of trials within k standard deviations of the mean" is what 1- 1/k2 gives, you are completely correct!

Last edited: Sep 21, 2008
3. Sep 20, 2008

Chebyshev's Theorem does indeed state give the percentage data you can expect to find within $$\pm k$$ standard deviations of the mean, as long as $$k > 1$$ (and it is here.
However, remember that technically the answer is a lower bound, so you the proper response not that the percentage is $$75\%$$, but that it is at least $$75\%$$.