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