Final answer:
When determining the mean of the remaining 4 observations after subtracting the sum of (n-4) observations from the total sum, none of the provided options correctly represent the mean of these observations based on the given information.
Step-by-step explanation:
The A.M. (arithmetic mean) of n observations is m. If the sum of the (n−4) observations is a, then the total sum of all n observations is nm, because sum equals the mean multiplied by the number of observations.
To find the combined sum of the remaining 4 observations, you subtract the sum of the (n−4) observations from the total sum: nm - a. The mean of the remaining 4 observations is the combined sum of these 4 observations divided by 4, which is (nm - a) / 4.
We know that the mean is m, which is a hint towards our solution. By substituting m with nm/n, and then factoring out n from the numerator, the equation simplifies to (n(m - a/n))/4.
This does not directly match any of the options provided. Upon inspection, one may conclude that there might be a mistake in the options or the question itself, as none of the provided options seem to correctly represent the mean of the remaining 4 observations.