Chebyshev’s Theorem

Write a paragraph to describe Chebyshev’s Theorem to a friend that knows very little about statistics.

16 Responses to “Chebyshev’s Theorem”

1. ~leimccvr Says:

The theorem states, that if you find a value of 1-1/k^2 that you have a standard deviation. This information is true of data set no matter what. If the data is skewed this theory will work. k id the number of standard deviations from your mean of the data.

2. ~leimccvr Says:

The theorem states, that if you find a value of 1-1/k^2 that you have a standard deviation. This information is true of data set no matter what. If the data is skewed this theory will work. k id the number of standard deviations from your mean of the data. The data is represented in intevals.

3. libmath12nd Says:

I do not understand. What is a standard deviation? How does this apply to the theorem?

4. tpdunn Says:

Standard deviation is used to to describe the spread of data around the mean. It applies to Chebyshev’s Theorem because Chebyshev’s Theorem finds what proportion of data lies within a certain number of standard deviations on either side of the mean.

5. hunnyroastedpeenut Says:

Let’s say that there is an survey done and you have your results. If you find the mean, or average, of your results you are just finding what is in the middle. But, what if you want more than just what is the average? And you want a little more accuracy? You would need to include a little more information to accurately represent what the actual results are. Well, by using standard deviation you can find by how much to the left and right of your mean you should go to include that little bit more information. Chebyshev’s theorem tells you how many standard deviations you should go according to how accurate you want to be. For example, if you want about 75% of your data included you would want to move left and right 2 standard deviations. If you wanted more data, that falls closer to 88.9% of your data to be included, then you would want to move to the left and right 3 standard deviations. If you wanted 93.8% of your data to be included then you would need to move to the left and right of your mean 4 standard deviations. Using standard deviation and Chebyshev’s Theorem helps surveys and experiments to be more accurate and represented so.

6. Crystal Says:

Chebyshev’s Theorem is any set of data (either population or sample) and for any constant k greater than 1, the population of the data that must lie within k standard deviations on either side of the mean is at least 1-1/k^2.

The concept of the data can be spread about the mean and can be expressed quite generally for all data distrbutions as in skewed, symmetric, or other shapes.

7. pandabear18 Says:

The Therom states that for any set of data and for any constant k greater than 1 the pop of the data must lie within k. 1-1/k^2.

No matter what the data is true.

8. pandabear18 Says:

I am not really sure how to explain math concepts that is why i am not going to be a math teahe ðŸ™‚

9. Crystal Says:

Like always which is really good!!
Go Catie! ðŸ™‚

10. libmath12nd Says:

pandabear18 : Part of the reason we are responding to these questions is to work on improving our math vocabulary, sharing our thoughts and organizing our thought processes.

11. ~leimccvr Says:

I agree with Tyler as to what a Standard Deviation is. To represent the data I would say that suppose I have numbers such as heights of people around the world. I would find the average of those heights, and I would apply the Chebychev’s theorem to figure out how much those heights differ from the average. And what percentage differs.

I am not sure how to explain it better, sorry.

12. Edocsil Says:

I would have to agree with Tyler also. Chebychev’s theorem is used to give you an area of data that the majority of the data is located so you can get an idea of the deviation, whether of not it is centered.

13. hunnyroastedpeenut Says:

I think tpdunn did a great job explaining this concept. It’s short sweet and to the point…unlike mine! I think I may be overthinking it or something. But you did a great job tpdunn!! ðŸ™‚

14. tpdunn Says:

Thanks, I thought yours was good as well. It had more thought put into it than mine.

15. edocsil Says:

The point of Chebychevâ€™s theorem is to show you were the majority of the data falls within a certain set. and allows for to see how teh data is spread out.

16. burymewithit Says:

Chebychev’s Theorem is s a concrete way to expect the data to fall in certain parameters in any type of distribution.