Chebyshev's Theorem
3 important questions on Chebyshev's Theorem
What is the Chebyshev's theorem?
A rule of thumb that can tell us something about the spread of the data by pointing out the relationship between the % of data and std as follows:
The % of the data that lies within "K " standard deviations is atleast: 1 - 1/k^2 of K > 1.
The % of the data that lies within "
How do you interpret Chebyshev's theorem?
Using the definition discussed in Mathtutor videos:
The % of the data that lies within "K " standard deviations is atleast: 1 - 1/k^2 of K > 1.
K is the number of standard deviations. So if K = 2, then the % of data that lies within 2 standard deviations is atleast:
1- 1/2^2.
So that is 1 - 1/4 = 3/4 which is 75%
If k = 3, then the % of the data that lies within 3 standard deviations is:
1 - 1/3^2 = 1 - 1/9 = 8/9 = 88.9%
The % of the data that lies within "
1- 1/2^2.
So that is 1 - 1/4 = 3/4 which is 75%
If k = 3, then the % of the data that lies within 3 standard deviations is:
1 - 1/3^2 = 1 - 1/9 = 8/9 = 88.9%
How can Chebyshev's theorem be viewed in relation to the emprical rule?
1) Not bell shaped data
In the same way that the empirical rule can be viewed as a rule of thumb for data that is bell shaped, chebyshev's theorem is similar but for data that is not bell-shaped.
2) Where the empirical rule can tell us that a % of the data falls within x stdeviations of the mean, Chebyshev can only give us a minimum amount, like "atleast x percent is gonna fall between one standard deviation".
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