Final answer:
The false statement is d, which inaccurately represents the positions of the mean, median, and mode in a distribution; their relationship varies depending on the distribution's shape.
Step-by-step explanation:
The false statement among the provided options is d. It claims that the median is always closest to the mode and the mean tends to be farther out on the tail. This statement is not universally true. The positions of the mean, median, and mode on a distribution depend on the distribution's shape.
In a symmetrical distribution, the mean and median are indeed both centrally located and are the same, but this does not necessarily mean they are close to the mode, unless the distribution is perfectly normal. Therefore, the mean may not always be farther out on the tail. For skewed distributions, the mean is typically drawn towards the tail, and the median lies between the mean and mode.