| 21. | The rules are based on the mean value and the standard deviation of the samples.
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| 22. | The mean value and standard deviation are undefined.
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| 23. | Another proof can be given by combining the mean value theorem and the intermediate value theorem.
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| 24. | It can be generalized to more variables according by the mean value theorem for divided differences.
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| 25. | Haldane assumes 30 to be the mean value.
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| 26. | Otherwise an representative mean value has to be considered; for more, see the equations section below.
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| 27. | A higher ratio therefore implies that the samples were drawn from populations with different mean values.
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| 28. | These refinements of Taylor's theorem are usually proved using the mean value theorem, whence the name.
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| 29. | This means that the response of the filter depends on the mean value of the signal.
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| 30. | In particular, the ultrahyperbolic equation satisfies an analog of the mean value theorem for harmonic functions
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