Question

In its role as a balance point, the mean balances

a) the distance of the largest observation against the distance of the smallest observation.
b) the combined distance of all observations above the mean against the combined distance of all observations below the mean.
c) the number of larger observations against the number of smaller observations.
d) all of the above

Answer 1

The correct answer is option b), the combined distance of all observations above the mean against the combined distance of all observations below the mean.

Step-by-step explanation:

The mean acts as a balance point by equalizing the total distances of all observations above and below it, rather than corresponding to the distance between the largest and smallest or the count of larger versus smaller observations. In essence, the mean is a balance point that makes the total distance of all observations that lie above it equal to the total distance of all observations that are below it.

This property holds true for symmetrical distributions, where the mean, median, and mode coincide at the center. However, for skewed distributions, the mean is affected by extreme values or outliers more than the median and mode, causing it to move toward the tail of the distribution. Therefore, it does not necessarily balance the distances between the largest and smallest observations or the number of larger observations against the number of smaller observations.