Lower bound of weighted average of sequence

1. What is the meaning of a weighted average?
2. What is the difference between average and weighted average?

What is the meaning of a weighted average?

A weighted average or mean is one where each item being averaged is multiplied by a number (weight) based on the item's relative importance, rather than treating each item equally. The weights or weightings are the equivalent of having that many similar items with the same value involved in the average.

What is the difference between average and weighted average?

In calculating a simple average, or arithmetic mean, all numbers are treated equally and assigned equal weight. But a weighted average assigns weights that determine in advance the relative importance of each data point. A weighted average is most often computed to equalize the frequency of the values in a data set.