Chebyshev theorem

Chebyshev's theorem

1. Chebyshev’s Theorem

2. Relations between the Mean and the Standard Deviation The mean is a measure of the centrality of a set of observations. The standard deviation is a measure of their spread. There are two general rules that establish a relation between these measures and the set of observations. The first is called Chebyshev’s theorem. The second is the empirical rule.

3. Chebyshev’s Theorem At least three-quarters of the observations in a set will lie within 2 standard deviations of the mean. At least eight-ninths of the observations in a set will lie within 3 standard deviations of the mean.

4. Chebyshev’s Theorem In other words,

5. The Empirical Rule If the distribution of the data is more or less symmetrical (normal distribution), then: Approximately 68% of the observations will be within 1 standard deviation of the mean. Approximately 95% of the observations will be within 2 standard deviations of the mean. A vast majority of the observations (all, or almost all) will be within 3 standard deviations of the mean.

6. Problem Check the applicability of Chebyshev’s theorem and the empirical rule for the graduation percentages of your batch-mates .