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 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.
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.
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.
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.
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 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.