Artificial intelligent assistant

Mean of a distribution In an asymmetrical distribution the mode and median are respectively 12.30 and 16.42. Find the mean of the distribution.

Without additional information about the distribution, there is not much that we can assert **for certain**. However, if we are willing to make reasonable guesses, there is often a rough empirical relationship between mode, median, and mean, for fairly well-behaved unimodal distributions. The relationship is $$\text{mean}-\text{mode}\approx 3(\text{mean}-\text{median}).$$ We can use this approximate relationship, combined with a crossing of the fingers, to estimate the mean, though an answer to $2$ decimal places would certainly be inappropriate!. There are even proofs that under suitable restrictions the relationship roughly holds.

For a detailed discussion at a not difficult level, please look here.

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